Indeed, Linux in Wolfram cloud prints for 1/(-1.)^1.2 (after copy paste of the answer)
-0.8090169943749475+0.587785252292473 I
while windows prints
-0.8090169943749475 + 0.5877852522924731 I
Yep. Both of them have an error, as N[1/(-1)^(12/10), 50]
-0.80901699437494742410229341718281905886015458990288 + 0.58778525229247312916870595463907276859765243764315 I
So it should be 74 not 75 and 731 must be in both cases. I suppose you use Intel C++ compiler math library, since it is the only one that has complex numbers apart from glibc?
Found an error in much more complex https://mathematica.stackexchange.com/q/282358/82985