I doubt the cable is bad though it's possible for cables to seize up in the housing if they begin to rust and corrode.
When you take that drumss apart, verify that the lever that the cable attaches to is able to achieve it's full range of motion. You should remove all parts from the drum, clean up all contact surfaces and replace the necessary springs + pads; machine rotors if they are warped. Compare the parts to check against warp/bent/damage and replace as necessary.
Left & right cables meet at the balancer and so it may be possible for one side to throw the other off. Whenever you service brakes, they should be serviced in pairs. Wasn't sure what was going in my case until I got a look at the parking brake cable balancer which was cocked-off to one side. Cable was slack at the drum and the lever on the drum totally seized. Prevented that wheel from engaging it's P-brake. | 
