Looking up the Alienware M11x's specs on Dell's website, it appears that you are running with an integrated/discrete setup composed of Intel Integrated Graphics and the nVidia GeForce GT 335M.1
From Dell's website:
With the Alienware™ M11x gaming laptop, you can play anything, anywhere. While weighing in at less than 4.51 pounds, the M11x packs enough power to handle the latest games. It truly redefines the gaming capabilities of sub-15" laptops.You can also maximize battery life by switching to integrated graphics or switch to the 1GB NVIDIA® GeForce® GT 335M graphics for an intense gaming experience.
This kind of setup comes with nVidia Optimus technology, which, sadly, only runs on Windows 7.
However, all hope may not be lost. There is an open-source alternative: Bumblebee. It is available as a PPA.
For detailed information on how to get nVidia Optimus cards working on Ubuntu through Bumblebee, see How well do laptops with Nvidia Optimus work?
Once you install Bumblebee, you should restart. After you've rebooted, you will be able to run programs on the nVidia card with the terminal command
Test that it's working properly by opening a new terminal window with Ctrl+Alt+T and entering
The above command will start glxspheres, a program which consists of a ton of 3D spheres. Additionally, if you look back at the terminal, you should see the word nvidia in the GL vendor string. Congratulations, Bumblebee's installed correctly and you can now use your nVidia card for graphics-intensive programs such as games.
I personally have a laptop with the nVidia GeForce GT 540M and Bumblebee effectively replicates the behavior of Optimus. An added bonus is that, like Optimus, Bumblebee turns off your nVidia card when you're not using it, so you'll get a better battery life than you would without Bumblebee.
1 Whatever you do, do not install the proprietary nVidia drivers from nvidia.com! This may totally mess up Ubuntu!