You did not say what the initial conditions are. But Mathematica DSolve
can solve it. The solution is complex, so I plotted the real part below.
ClearAll[m, x];
eq = m'[x] == (70 m[x] (1 + 125/1000 m[x]^2) (1 + 125/100 m[x]^2))/((200 + 140 x) (1 - m[x]^2))
sol = First@DSolve[{eq, m[0] == 1}, m[x], x]
Plot[Re@Evaluate[m[x] /. sol], {x, 0, 20}, PlotRange -> All]
There is a second solution also given by DSolve
to look at. The above is just the first one.
ps. not good idea to use user defined UpperCaseVariables or Symbols in Mathematica.