Let a curve $y=y(x)$ pass through the point $(3,3)$ and the area of the region under this curve, above the $x$-axis and between the abscissae 3 and $x(>3)$ be $\left(\frac{y}{x}\right)^3$. If this curve also passes through the point $(\alpha, 6 \sqrt{10})$ in the first quadrant, then $\alpha$ is equal to $\_\_\_\_$