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 $\_\_\_\_$.