Ignore the fact that you've gone straight to Chamber 11 from Chamber 6 (it's all part of the story, so just roll with it).
This'll cause you to fall through and land on a platform holding an Experimental Cube. Pick it up and carry it to the left-hand corner where the laser beam is powering up the transportation beam. Set it down so it's obstructing the beam, drop a portal nearby and then walk through it, this'll drop you back at the top end of the room.
Walk over the jump plate and it'll carry you through the portals and over to the Displacement Cube (haven't seen one of those in a while). Pick it up and then set it down beside the Experimental Cube.
Look for the beam receptor near the lifts on your left and use your portals so the beam from the Displacement Cube is directed at the receptor (use the small vertical corner to guide the beam properly).
This will cause the first of the two lifts to lower to the ground, so stand on it and then face the Displacement Cube up ahead. Note the colour of the portal you used near it and fire this portal anywhere else, this'll break the laser beam and raise the platform you're currently on.
Once it's pressing the switch, step onto the second platform and then use a portal to break the transportation beam completely. This'll cause the platform to raise upwards and let you escape via the exit.