Hi,
Here is a link which details the removal of the palmrest keyboard for your laptop. I suspect that it is not what you are after as it does not show the keyboard being separated from the palmrest.
With the assembly removed from the laptop perhaps you will be able to ascertain how to separate the two components. Hopefully it still will be of some use to you.
http://blog.parts-people.com/2014/12/01/dell-inspiron-11-3147-3000-series-palmrest-keyboard-removal-and-installation/