Let the maximum value of ( sin^-1 x)^2+( cos^-1 x)^2 for x ∈[-(√ 3)/2, 1/(√ 2)] be m/n π^2, where gcd ( m, n )=1. Then m + n is equal to ____.

Let the maximum value of $\displaystyle \left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$ for $\displaystyle x \in\left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\right]$ be $\displaystyle \frac{\mathrm{m}}{\mathrm{n}} \pi^2$, where $\displaystyle \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$. Then $\displaystyle \mathrm{m}+\mathrm{n}$ is equal to $\displaystyle \_\_\_\_$.