What exactly broke with your cables, one side turns while the other doesn't (internal fracture), or something else? If you can remove the cable core, you might be able to have the fractured part welded (as long as the weld won't be in tight turn) and it is ground smooth after. Just a thought...You'd be amazed how fast that cable turns when the car's dooing 50+mph; I believe about ~2000+rpm, so it has to be done right.

Anyway, time to start looking for a new odometer; if you can't fix it. Take out the odometer and look at whichever odometer is stuck around the 10 multiple and check for wear or anything out of place. Sometimes a little bit of teflon grease on the gears and pushers/slides will do the trick; unless something is actually broken or cracked. If you decide to try lubrication, do it carefully so you don't see splots on your odometer's numbers; a small cuetip, or toothpick might work.

ATLD