This has come up before here, and there were a lot of different complicated suggestions.
I had the same problem and it was solved by one cable TV installer who was familiar with the problem.
He had me buy a Radio Shack adapter (NOT filter -- it doesn't work for this) used to connect when you only have the two-wire 300 ohm input on the TV and need to attach the 75 ohm cable plug. It is about 4 or 5 inches long. One end has the two antenna connector wires, and the other end has a male cable plug. You also need the small plastic adapter the other way -- the one that has two screw connectors for the two wires and a female cable plug. Attach that to the Radio Shack adapter, then put it between your cable wire and your TV or cable box, and you're in business.
Sorry for the lack of technical knowledge in describing this -- all I know is that it works. I have no idea why, but I don't have hum. When I take it off -- hum.
If you can't find the adapter at Radio Shack based upon my inartful description, e-mail me and I'll drop by one near me and see if I can find it and get a part number for you.
--Neil