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There are two usual sources of hum: ground loops in the audio chain and RF interacting with power supplies.
Audio should have a one point ground meaning that it is grounded at a single point. Often this is not practical and it has been reported that using a ground isolator (from Radio Shack) is a good solution.
RF can interact with power supplies which can cause hum, especially “wall warts”. Solutions include using snap on ferrite rings on power leads but the most reliable solution is to keep wall warts and transmitters separated as far as practical. Sometimes just a few feet will work, other times larger distances are needed. Enclosing FM transmitters in a metal box usually helps. Not so much with AM since the signal is much stronger than FM.
That, in general, is an overview of the hum problems for part 15 stations but if you are having this problem there may be other causes.