What have you got to lose?
Use a low wattage fine point iron , 15 watts (or less), clean 1/8" (or less) at the end of each broken wire and lightly "tin" the ends, after the ends cool, apply a very small amount of paste rosin to the tinned end of each wire. All you have to do now is hold each wire in place and "touch" the iron the the soldering point for 1/2 a second.
As you can probably tell, less is more!
Ap