Area Under The Curves

If the area enclosed by the parabolas \(\mathrm{P_1:2y=5x^2}\) and \(\mathrm{P_2:x^2-y+6=0}\) is equal to the area enclosed by \(\mathrm{P_1}\) and \(\mathrm{y=\alpha x,\alpha > 0}\), then \(\alpha^3\) is equal to ____________.