The GE Smart Switch #12724 does not wire up the same as a normal switch. Without using a meter to verify your Line (hot) lead I am guessing at this. If it is the only switch I would try this:
The wire that is stripped in the middle is possibly Line ( so it goes on the screw labeled line on the GE switch.
The other black line is possibly load. so it goes on the screw labeled load on the GE switch.
Take the white jumper that came with the switch and connect to the bundle of other white (neutral) wires in the box.
Leave the traveler screw covered with tape.
Connect your ground.
It would be best if you got a cheap meter or one of those power detectors that you hold up to the wire that either beep or lights up if power is on the wire. Use it to find your hot!!
You do this at your own risk as I am not an electrician and recommend you verify the wiring. I used a meter and checked everything at the switch and in the light fixture. Then labeled it how I wanted to connect it. Taking pictures is also highly recommended so you have a reference to go back to.
This topic has a basic drawing towards the front which I think is like what your trying to do.
Hope that helps make it clear as mud! 