The break is likely right at the point where the wire enters the earpiece. That would be a difficult place to solder it together, I had the same problem with the sound cutting out to my Freedom Sprint earbuds. The wire was broken where it entered the right earbud.
1. Disassemble the right earbud. (or whichever one has the broken wire.)
2. Cut the individual wires close to the strain relief and temporarily leave them soldered to the the circuit board.
3. Carefully pull the strain relief down along the good section of cable towards the other earbud.
4. Strip the outer cable jacket back about 1-1/2 inches.
5. Don't try to strip the insulation from the ends of the wires. Just pre-tin them with solder. The insulation will melt back out of the way.
6. Un-solder the old wires from the circuit board one at a time and replace them with the new wires.
7. Pull the strain relief into position near the end of the outer cable jacket. Secure into place with a tiny bit of super glue.
8. Reassemble the earbud