Update: Recently I install kubuntu 13.10 and there is no problem with graphics. It just works fine out of the box.
I've seen many blog posts on how to make AMD HD7670M work on Ubuntu 12.04, specially when its in switchable graphics board like Dell Inspiron 15R 5520. I tried many things to make it work so that I could use the cinnamon desktop on ubuntu & other things too.. But to my surprise even the drivers from AMD site didn't work.
Then I tried a combination of those blog posts I read & somehow I became successful in running the full graphics including compiz settings inside My Ubuntu Machine.
Following are the steps I followed & it worked...
1. Create a backup of your xorg configuration file:
sudo cp /etc/X11/xorg.conf /etc/X11/xorg.conf.BAK
2. Remove/purge current fglrx and fglrx-amdcccle :
sudo apt-get remove --purge fglrx*
3. Install the driver:
sudo apt-get install fglrx fglrx-amdcccle
4. Install additional components for advanced graphics:
sudo apt-get install xvba-va-driver libva-glx1 libva-egl1 vainfo
5. Generate a fresh xorg.conf:
sudo aticonfig --initial
Take a deep breath....
The graphics should work now...
In case you still have problem getting them to work, make sure you have following lines in the /etc/fstab
tmpfs /dev/shm tmpfs defaults 0 0
none /sys/kernel/debug debugfs defaults 0 0
Hope it helps :)