I don't really have any issues with soldering / splicing the cable to investigate, but if Ubi has a replacement policy for these types of things I don't want to void my opportunity at getting a genuine new replacement. The mold around the two ends (the USB end and the breakaway end) seem pretty solid, not sure how anything could separate or short in there.
While the cable looks to be in perfect condition - and I certainly can't recall pulling or bending it in any sort of way between the last time it worked and then didn't - my guess is that it has to be something to do with the braided cable inside. The larger part of the cable works with a different "dummy end". The larger "smart" part of the cable isn't in question. It's definitely the shorter "dummy end" of the cable, the part that connects to the USB port. If the A/D box is bad or the break is too close this may not work, but if it is just broken wires in the cable lead, this may get you a working cable. and try soldering on a new plug (or even a cable extension with a plug). Audio Cable - PS3, PS4, Xbox, PC & Mac - Profetia. leaving plenty of lead from the little A/D box. rocksmith Floare de ora Aliat sugera Ubisoft Rocksmith Real Tone USB 11.25ft.
and know the long portion of a cable is bad. If it is the long portion, then you will need to buy a whole other cable. You may be able to buy these little parts separately.
New retail versions will hit shelves at the same time which will include access to the free update as well as 6 bonus downloadable songs included for free for new players. If it is the little portion, you could try replacing it with the end off of another xbox/ps controller. Rocksmith is faster than ever with a free downloadable update for Rocksmith 2014 Edition coming October 4th, 2016.