Learjet 31 Captain reported an uncontrollable pitch trim system caused an altitude deviation. Flight crew reset the pitch trim and returned to assigned altitude.

Narrative

While departing Runway XX at ZZZ and after landing gear retraction the aircraft was experiencing a failure to respond to pitch commands. The nose pitched to approx. 18 degrees and I was exerting some 60-80 pounds of forward push on the yoke to keep from stalling the aircraft. I was unable to level off at the 1500 MSL altitude as depicted on the SID. I performed a system reset using the primary trim switch. I was then able to trim the aircraft but at that time we were already at approximately 2500 MSL. I lowered the nose in case there was traffic above but as I later learned there was no loss of separation between myself or any other aircraft. At the same moment my First Officer (FO) was contacting Departure Control and was informed of our deviation and to standby to copy a phone number; which we complied with. It was a very hectic 90 seconds of activity trying to control an aircraft with a flight control malfunction which I reported to the Controller but was told she didn't care. This altitude deviation was by no means intentional and I am glad there was no loss of separation. I'm guessing I'll have to start working out more so I'll have more oomph to push but I would rather there not be a next time.