ZAB Controller described a loss of separation event when a PHX departure was issued an interim altitude for separation from overflight traffic; the clearance read back was not confirmed and separation was comprised.

Narrative

Aircraft X was a departure off PHX and given the control instruction to climb to FL360. Aircraft Y was above Aircraft X and level at FL360. This situation was quickly recognized; and Aircraft X was told to amend the altitude and maintain FL340. Aircraft X never read this clearance back and continued a climb to FL360. Aircraft Y was given a turn of 90 degrees. Aircraft X was told to maintain FL350; however the sector was so busy the first transmission was blocked. Positive separation was regained shortly. It should be noted that training was taking place on both the R-Side position and D-Side position. The sector was very busy and had been for some time. The R-Side training team had to ask the CIC for a D-Side; as the supervisor was not present in the area. My D-Side training team was pulled off another sector to staff the D-Side position on the sector where the incident occurred. Had the sectors been De-combined; this incident would not have occurred. Aircraft X was issued a safe altitude to maintain twice but did not respond. Recommendation; the supervisor in the area should have been more cognizant of the situation developing on the sector and the amount of traffic that had been transitioning the airspace. These sectors should have been De-combined.