Replacing the "bridging" cable?

I have a set of MPow H5 headphones. They fell on the part that holds the swivel by the right ear cup broke. I was going to repair it using a carbon fiber kit I have to overlay the broken part.

The thing is that in the process I nicked the cable that bridges the left and right ear. The cable is 8 conductor ( as far as I see or more ). Is there any way to repair it?