If the area enclosed by the parabolas $P _ { 1 } : 2 y = 5 x ^ { 2 }$ and $P _ { 2 } : x ^ { 2 } - y + 6 = 0$ is equal to the area enclosed by $P _ { 1 }$ and $y = \alpha x , \alpha > 0$, then $\alpha ^ { 3 }$ is equal to $\_\_\_\_$.
If the area enclosed by the parabolas $P _ { 1 } : 2 y = 5 x ^ { 2 }$ and $P _ { 2 } : x ^ { 2 } - y + 6 = 0$ is equal to the area enclosed by $P _ { 1 }$ and $y = \alpha x , \alpha > 0$, then $\alpha ^ { 3 }$ is equal to $\_\_\_\_$.