Those Bell fix kits are only appropriate for getting Wal-Mart level kids bikes back in usable condition. If you are on a budget, any bike shop will have bulk cables (usually Jagwire or similar basic stainless cables) and bulk housing you can buy by the foot. My LBS throws in the cable ends and ferrules but other shops might charge you an extra buck or two. Even these basic cables and housings are a couple steps up from the Bell fix kits and you will notice much smoother and sharper shifting and less mushy braking. Remember that, unlike the Bell kits, there will be a difference between the shift and brake housings so don't get them mixed up.

You can also buy Jagwire or Shimano kits to re-cable your whole bike. Some get pricey for the ultimate in smooth performance, but most riders are happy with the mid-priced cables. As I said, if you have been happy with the Bell cables, even the entry level bulk LBS cables will put a smile on your face. If better cables with new housings keep breaking at the same place, look for a problem in routing or the shifter.