If you fix the broken wire, make sure you also fix the root of the problem. It looks like LG started adding a thick sheet of clear plastic at first, and now the newer models ship with tar that has some type of fabric attached to it This prevents the wires from sinking into the tar, and absorbing so much heat that they end up melting/breaking apart. (I assume. I don't have any official comments from LG)
Some techs have been known to throw a large piece of thick plastic between the wires and the tar. I bet fiberglass insulation would do the trick also, as long it doesn't have any ignitable paper on it.