In the old days, you could easily repair headphone cables just by stripping back the insulation on the wire at each side of the break, twisting the bare wires together, and wrapping insulation tape around them.
However there seems to be a new type of wire in modern headphones - there doesn't seem to be any insulation and the wires themselves feel a bit different, and they don't start working once you twist them together. Is there a way of performing a similar repair on this type?