Let $y=y(x)$ be the solution of the differential equation $\left(1-x^2\right) d y=\left[x y+\left(x^3+2\right) \sqrt{3\left(1-x^2\right)}\right] d x,-1< x<1, y(0)=0$. If $y\left(\frac{1}{2}\right)=\frac{m}{n}, m$ and $n$ are coprime numbers, then $\mathrm{m}+\mathrm{n}$ is equal to