General aviation single pilot jet Captain reported a terrain warning during climb in mountainous terrain resulting from an altitude communication issue with ATC. The Captain turned to avoid the highest terrain; then resolved the ATC communication issue and received climb clearance above the terrain.

Narrative

Being very familiar with the area; I filed an IFR flight plan out of DRO with a westbound terrain avoidance pathway taking into account the chain of 18k mountain peaks north of the airport. I was given a clearance on the ground #1 for departure runway 21 as filed climb and maintain flight level 260. At approximately 3 min into the flight climbing through 10;500 ft I received ATC instructions cleared direct DBS VOR; 11;000 ft which I read back. I assumed the level off was for traffic but noticed it had me pointed directly towards the mountains. I anticipated a new climb clearance shortly thereafter. I also noticed the controller voice changed thereafter; and he was very busy at the handoff. Out of courtesy; I waited a few minutes but then thought they may have forgotten about me; so I then called ATC 'Denver; Aircraft X; 11000 ft; request higher'. I received no response. I waited a few additional minutes; but controller was busy handling other aircraft. I could see the mountains approaching so decided I needed to deviate left of course to avoid terrain. At that moment I also got a terrain warning from my panel; so I switched to heading mode and made an approximately 30 degree heading change to the left and immediately notified ATC; 'Denver; Aircraft X; deviating left of course for terrain' The controller verified I had terrain in sight and then cleared me to deviate. He then asked if I had not been cleared to flight level 260. I responded that that was my initial clearance; but it had been changed to 11;000 ft by the last controller. I was then also cleared to climb to flight levels and navigate to the next waypoint. At the time I did not really understand why the controller had given me more direct routing but a restricted altitude that was not shortly thereafter modified. Upon landing I spoke to the controller who stated that he wanted to discuss what appeared to be a problem with communication on my departure. He stated that my new clearance on departure was 'upon reaching 11;000; cleared direct DBS; but I had read back direct DBS; 11;000.' I then asked why the controller did not correct my readback if it differed from what the instructions the controller had intended but was not given a clear answer. He stated something to the effect that even airline pilots sometime readback a shortened version of the clearance. In retrospect; if I had understood the clearance correctly; I was still cleared to climb to flight level 260 after my turn and that is why ATC still believed I was cleared to that flight level. In my mind; however; I was following my last issued clearance limit of 11;000 feet. Unfortunately; when I called ATC to try and get a higher altitude; which would have probably cleared up the miscommunication; I could not get a response in time; so I had to take affirmative action; commanding a course deviation; to ensure continued safety of the flight. Since it was VFR weather conditions; I felt safe maneuvering; and did not feel that we were in immediate enough danger to declare an emergency. If I did not receive a follow-up response from ATC; I was preparing to follow lost communications procedures and return to my initial flight plan fixes that took me away from the mountains. My conversation with Denver on landing I thought was informative and gave me insight as to what went wrong; as I think at the time; both ATC and I were confused. Fortunately; I felt that my training took over and I was able to command the flight to safety without incident. I discussed the event with my instructor immediately after my call with Denver for further debrief. In conclusion; I agree this was a problem with miscommunication; and intend to focus on further improving my readbacks to include all the necessary detail to make sure that I as a pilot and ATC have a mutual and clear understanding of the flight.