Does any one know if the new taillights fit the 2011 model?
It does and it doesnt.
Allow me to explain, mechanically it is plug and play, the housing mounting system is exactly the same
(ie screw locations, tabs and notches all the same for 2007 to 2014 models, just go to eBay and search CX-9 tail light parts, you'll see the mechanical backsides are all the same).
Electrically, it's a different story, you have to cut and splice the connectors. 2013 and up models are not OEM LED like previous years. I put in 2009 OEM LED tail lights in my 2013 CX-9, looks much better IMHO, very easy swap except for cutting and soldering of the 2009 plugs into my 2013 wire harness, process is vice versa, if you want to put 2013 into 2011 model, it will fit but have to change the connectors.
here's proof it fits, 2009 LED tail lights in a 2013 CX-9 with modified LED bumper lights :
one caveat though for the original poster asking about going from 2011 to 2013 tailights
there are two lights in the tail light that does not light up in 2010-2012 CX-9s
(Mazda cost cutting took out the bulbs)
these light up in 2007-2009 / 2013-2014 CX-9s
so if you have a 2011 you may not have wires to light up these two bulbs if switching to 2013-2014 lights
(see illustration below)
no light bulbs in 2010-2012 CX-9s