For everyone who wants to know if the black cable fixed my problem: I haven’t tried it yet.
I found where the break is located in the original black cable and I fixed the connectivity by re-bending the cable. See: Black Cable Hack for Voiding Warranty
The instructions for replacing the cable are straightforward, but the steps are pretty complicated. In particular, there is a lot of double-back tape and you have to be really careful with the alignment. I don’t expect my “re-bend it” solution to work forever, but until it fails, I’d rather get as much life out of the old cable as possible.