  We have carried out an ultrahigh field cyclotron resonance study of $n$-type
In$_{1-x}$Mn$_x$As films, with Mn composition $x$ ranging from 0 to 12%, grown
on GaAs by low temperature molecular beam epitaxy. We observe that the electron
cyclotron resonance peak shifts to lower field with increasing $x$. A detailed
comparison of experimental results with calculations based on a modified
Pidgeon-Brown model allows us to estimate the {\em s-d} and {\em p-d} exchange
coupling constants, $\alpha$ and $\beta$, for this important III-V dilute
magnetic semiconductor system.
