YouTube has some pretty good instructional videos on how these things work and how to replace broken cables. I expect if you have that much play in the cable, it has detached from one of the anchor points on the slide, not broken.
Look carefully at the wall of the slide where it comes in contact with the wall when extended. They cover those thing pretty effectively with trim over framework wit the motors and chains hidden behind the trim pieces.
horsedoc
2008 Damon Essence
2013 Jeep Sahara Unlimited
Blue Ox tow