1. Cut off both chewed ends in the middle of your cable until you have two fresh and clean ends.
2. Deisolate.
3. put some heat shrink tube on one part of the cable, so that you can push it to the area where you soldered later.
3. Solder the cables back together.
4. push the heat shrink tube over the soldered area, shrink it. (using heat.)
et voilà: works good, looks good.