will soldering work on lcd cable

The Macbook Air mid 2009 A1304 13" is one of those with the hinge issue that plagued so many. I've got one here. Replacing the hinge is no problem, but I found while digging into the left hinge that the LCD cable has been damaged. Two of the thin wires in the cable bundle have severed (due to the hinge breaking and then excessive movement of the LCD display).

My question: will soldering these thin wires work? That is, will the signal carry through?

Has anyone dealt with this before, and if so, any advice on how to secure the cable after soldering to help it from breaking again?

I'll attach a picture. Thank you.