You don't have to pry it in such a way that it busts the latches and then your tailgate won't stay shut!
If you look along the inside edge of the tailgate, you'll see that the latch is like a little tooth. When you lift up on the handle, via cable action, it retracts and allows the tailgate to swing down. Probably you jacked up the cable, so take a big, long screwdriver and push it into the crack between the tailgate and truck, and manually push that latch in.
If you're lucky, like I was, the cable only broke on 1 side, and you still can lift the handle to free the other side. Otherwise, you may need to get someone to pry one side while you do the other, or use 2 screwdrivers and keep one wedged in place while you pop the other side.
Yes, you'll have to do this every time you want to open the tailgate (unless you want to replace the cable) but my 12-year-old truck has been like this for a long time and it's really not so bad once you get used to it! I leave the screwdriver right in the bed of the truck ... in fact I gave it a name, "The Magic Screwdriver."
Oh, one thing I should warn you about is this problem seems to make your tailgate more likely to fly open unexpectedly (it won't open when you want it to, but when you don't ,,,,,) so make sure you secure your loads or you'll end up picking stuff up out of the road. Once I was hauling a particle-board bookcase that I had just snagged out of someone's trash when my tailgate flipped, the bookcase slid out, hit the road and exploded into about 50 million pieces! Luckily I was driving at night on a rural road, so there were no cars behind me or anywhere around as I cleaned up the mess and beat feet outta Dodge!
BTW, I believe a busticated tailgate officially qualifies your ride as a "redneck truck."