The TX modules are specific for to the radios. I use an M8 TX module in my M8. My RX receiver should not differ to your receiver I think.
But in the Spektrum DX3 transmitter doesn't have a module (or has it?). Even it had a module, it won't fit the M8 or M11. The M8 has other connection pins, so won''t fit. Just like I cannot use a JR-R1 module in my M8.
But maybe some people are that handy to built in the system in all kind of transmitter. I have taken a look in my TX module, and it is all hardware.
BTW: There is already a topic of the Spektrum system.