Flight Instructor on training flight with student reported a NMAC with another aircraft during descent.

Narrative

On a cross country lesson with a student flying westbound from ZZZ; under radar and radio contact during flight following from approach when we heard the approach controller trying to communicate with another aircraft. We noticed that the aircraft in question wasn't responding to the controller's multiple attempts. At this point we were approximately 10 nm SE of the MHT airport; above Manchester Class C airspace. We didn't get any traffic alerts from the controller but were looking for this traffic as we had them on our ADSB traffic map and it looked to be converging with us.While we were descending from 7500 ft. to 6500 ft. and heard no response from the other aircraft; I decided to disengage the autopilot as I didn't have visual contact with the traffic and advised ATC of my intentions to climb to avoid this traffic. As I climbed about 80 ft.; I saw the traffic and reported traffic in sight. I then continued on my intended path and descended to 6500 ft.; after which the pilot of the other aircraft finally responded to the controller as well. There was some radio back-and-forth between the controller and the pilot of the other aircraft as I continued on to my destination at 6500 ft.