Toilet doesn't totally flush, then drains, then gurgles up - thoughts?

[FlushTester]

Here is a video, as an explanation won't do this justice:

http://youtu.be/On9pIwF87Gs

We've tried plunging with two separate plungers.

Next thoughts are possibly trying a snake or some enzymes.

Nothing in the house that would suggest it is some solid object that was tossed down there.

 

[phishfood]

There is a clog in the line between the toilet and it's vent. The toilet needs to be pulled and the line snaked with a full size cutter head.