I just went through this a week ago with my odometer. Mine is also a cable driven unit. You'll want to read through the following link.
How to Repair Your Broken Odometer
I didn't feel comfortable removing the dial pointer on my speedometer myself. I took it to a shop where it cost me $400 to get it fixed. In retrospect, the above link didn't address my particular unit, since it didn't properly address the fact that I had to remove the dial pointer. The way to remove the dial pointer was to twist while pulling upward. I may have saved myself $350 had I known that. I tried to push it straight up.