A quick internet search revealed that the first and easiest fix is to connect the cable ground and the electrical system ground to the same ground rod. When I checked this out I realized they already are connected to the same ground rod, which should make a ground loop nearly impossible UNLESS THE CONNECTIONS ARE CORRODED! What do you know, the house is about ten years old, and the outside copper leads from both the breaker box and the cable TV are severely corroded where they connect to the ground rod.

Pulling them and cleaning everything eliminated the hum. So even if you haven't gone to the dark side and placed an LCD TV between your speakers it might be a good idea to check your electrical system's ground and clean it if it's corroded.