Yes,
The enamalled wire is becoming increasingly common. You basically need to burn this off to enable the solder to adhere.
Either with a lighter (a bit tricky) or using the solder iron (a bit easier) or a solder bath (easier but uses a lot of solder and not typically a diy task).
You do of course have to re-insulate any bare wiring as the enamel is the insulation (mass production economy I suppose). I'd suggest heatshrink over pvc tape.
It can be done, have done it myself and told others how to do it (no compaints so far) - but the manufacturers would say it's not a diy job and either a warranty repair of buy a new set
Steve