I was thinking of pouring some kind of leveling cement 1 inch thick is this possible.

I doubt that 1" of new concrete will hold. There are various theories about thoroughly scrubbing the old and using special epoxy for this but it still may not work.

There are concrete levelers that adhere to cement slabs.
http://www.dap.com/product_details.aspx?product_id=119
Concrete overlays are also available.
http://www.youtube.com/user/cntelevision?v=7veR81HkE_4&feature=pyv&ad=44040951 86&kw=cement%20overlay&gclid=CKLY1d6ky6YCFYpN2godF VYYHg