Helicopter pilot reported being notified by one of the passengers while departing a non-towered airport that an aircraft was turning near the helicopter. Reporter stated they did not see the aircraft and that it appeared to maneuver to avoid collision.

Narrative

Shortly after departing uncontrolled airport; generally heading to the northwest and climbing to my cruising altitude of 1500 feet MSL; the right aft passenger indicated a small plane close and at the same altitude was turning to go behind us then shortly after; the left aft passenger indicated the small plane coming out to the left aft side of our aircraft.I did announce my intentions but I never heard a reply (not to say the other aircraft didn't make radio calls) and I never saw the airplane that the passengers reported seeing (but afterwards they did indicate that they did not hear a radio transmission from the other aircraft either). Because I never saw or heard the aircraft; I have no idea if it was a single or twin fixed wing aircraft or the call-sign either. I think contributing factors for this were that I climbed to early to my cruising altitude instead of waiting to be further away from the airport which put me in the fixed wing pattern altitude. Also; I may have had the volume low and/or radio selector incorrectly set causing to miss radio transmissions on the CTAF frequency or radio transmissions could have been blocked by another frequency. Also; it was my second day flying this aircraft and I never saw aircraft on the PFD; MFD or the Garmin GTN radio; so probably the traffic alert settings on the electronic displays were set differently that what I'm used to. Also I had begun navigation so I was heads-down in the cockpit to handle that task.In hindsight; I'm very grateful the other aircraft had detected me in the pattern and took corrective action to prevent a mid-air collision (in VMC). I will definitely incorporate into my process deliberate altitude/distance situational awareness operating close-in to airports. Despite the passengers in my aircraft eventually seeing the other aircraft and informing me about it; this was a more reactive circumstance instead of proactive that would have allowed to take steps and maneuver to prevent getting close in the first place.