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Yes. I used to run a 9spd XT rear derailleur with an 11-34 XT cassette and Ultegra 6703 3x10 shifters (with an Ultegra 6703 30-39-53 triple chainset) and it worked a treat. Deeply unfashionable, with a triple chainset, but it gave an epic gear range.
Perfect for virtually guaranteeing being able to ride up Hardknott and Wrynose on the Fred Whitton, while still being able to hammer the descents and the flats.
Will this lot work together? I think they all have 1:1.7 ratio.
Shimano 10sp road shifters, Shimano 9sp slx MTB rear derrailer, shimano 9sp cassette 11-36