From the coloration, it sounds like a snap in the USB wires. The easiest way to fix this is to get wire strippers and electrical tape (Or any tape will work, I just prefer electrical in these cases. It insulates, and it sticks well). You can strip the wires until the metal is exposed, and twist the appropriate wires together. Then tape them back together. As long as metal touches metal, you should be good. Easiest solderless solution.
If you’d prefer to solder it, you can strip it, and then tin the wires (Because I doubt that you have solid core wire, it’s likely braided wire). This is done by melting a little solder on the tip of the iron, and then spreading the solder onto the frayed wires coming out of the insulation. By doing this, you’ll have made the end of the wire into an easy-to-work with tip. Do this for both sides, then place them end-to-end, and again, melt a little solder onto the tip as before, drip it in the gap, move the iron away, and let it harden. Then tape the two wires back together. The problem is that without the red and the black wires, you’re not getting any power to your stick! Big problem. Lol.