Are you using SRAM or Shimano?

Both of my road bikes have mtb cassettes and rear der on them.

My steel Gunnar Sport has 9 sp Ultegra triple with an XT 12-34 and XT RD. I've been riding this set up for about 10 years now. I've done some big Colorado passes with it, 10ft+.

My carbon fiber Spec Ruby has 10 sp Ultegra triple with SRAM 12-36 and XT Shadow RD. Works great!

My bf has set up several bikes for friends like this.

NOTE: to do this with a 10 sp set up and 11-36 you need to use a 9 sp Shadow RD. To use an 11-34 you should be able to use a 9 sp non-Shadow RD. The big thing here is that you have to use the 9 sp RD as the 10 sp RD will not work with the 10 sp shifters, I know that sounds strange, but it's true. I recommend a K-Edge chain watcher as the chains like to jump when you have the huge cassette on there. You'll need a new chain too as you'll need a longer chain than you probably have for all this.