When mine failed like this (a common problem) I soldered it back together like you did only to find that the overall wire was old and fragile and broke again right away. Ended up having to replace it.
Edit- new cable costs $66.
Brents347 Truckee, CA.
07 Yamaha R6
07 KTM 950 Super Enduro
04 KTM 250exc- plated two-stroke