cable repair

I purchased some Sennheiser HD650 headphones a while ago and accidentally broke the tip off my 3.5mm phone connector jack. Now normally this would be a pretty easy fix, just snip and re-wire but the problem is the cable is double-lead or whatever it is called. Basically it is two cords that are...

So I decided to try to open and solder my headphones after identifying the area of the problem, but when I opened the cable, it was not what I expected. I thought there would be 2-3 insulated copper wires and the solder would be easy, but when I opened them I found this (images attached), a...