Differential Equations: JEE Main 2024 Mathematics question

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