I had the exact same problem, which was solved by one cable TV guy who knew what to do (no jokes about morons, oxy or otherwise).
He sent me to Radio Shack to get a 75-300 ohm adapter. It is not the one they sell as a "filter," merely an adapter. (I tried the filter and it doesn't help.) I wish I had the part number, but it's not on the piece. It is about 6" long total. It has the male part of the coax as part of a 2" rectangular rubber piece with 4" of antenna wire and two spades extending from it. Then I connect it to a standard plastic antenna to coax converter, which has the terminals for the spades and the female coax. I don't know why it works, it's not made for this purpose, but it does. I have no more hum. When I take it off -- hum! (Hmm?) It costs less than $5. If you can't find it, post here and I'll try and check at Radio Shack for the part number. I hope it works. The cheapest solution to a BIG problem I ever found!
He sent me to Radio Shack to get a 75-300 ohm adapter. It is not the one they sell as a "filter," merely an adapter. (I tried the filter and it doesn't help.) I wish I had the part number, but it's not on the piece. It is about 6" long total. It has the male part of the coax as part of a 2" rectangular rubber piece with 4" of antenna wire and two spades extending from it. Then I connect it to a standard plastic antenna to coax converter, which has the terminals for the spades and the female coax. I don't know why it works, it's not made for this purpose, but it does. I have no more hum. When I take it off -- hum! (Hmm?) It costs less than $5. If you can't find it, post here and I'll try and check at Radio Shack for the part number. I hope it works. The cheapest solution to a BIG problem I ever found!