It is not that difficult to replace the auxiliary water pump on the E71. It is located almost on the same spot on the M as in the diagram that I posted for the 5.0. The part number is different for M model. This is the part number for the M.
11517629917
Auxiliary water pump
And the link to RealOEM.com -
https://www.realoem.com/bmw/enUS/sho...diagId=11_4390