nt.number theory - at which rational points does the Hypergeometric function take rational values

A generic example is ${}_2 F_1(frac{1}{3},frac{2}{3},frac{6}{5};frac{27}{32})=frac{8}{5}$. So my question: Is there any description of the set of rational points at which the hypergeometric function ${}_m F_n$ takes rational values?

The references to the literature where a lot of such examples listed are apreciated very much too.