How to repair broken garage door cable?

Well, as you have asked, I think you are asking for springs, Both extension and tension springs can be repaired, but not the safety cable, Garage door cable is also known as "Safety cable". It's for the garage door to avoid any incident in the future.

Moreover, other springs can be repaired you need to contact First Coast Garage Door they can help you in this matter, don't repair it your-self as you can injured yourself.

From the sound of it, you have two extension springs.
Lift from the side with the broken cable, not in the middle.
If
you still have trouble lifting it, you can have a friend or neighbor
lightly pull down on the other side while you lift the broken side.