Hi I have the Shimano slm 6000 10 speed shifter has a Shimano 10 speed chain I have the RDM 5120 Shimano rear derailleur I have cslg 10 speed 48 t cassette and it doesn't shift to the gears properly from what I read the m 6000 shifter is not compatible with the derailleur so I ordered the slm 4100 shifter is that going to work for my 51 20 derailleur and 10 speed cassette