i'm facing the following problem:
find the area of the set $M=\{(x,y): |x|^{\frac{2}{3}}+|y|^{\frac{2}{3}}\le 1\}$ using integration

i thought about only integrate where x,y both $\ge0$ and multiply by 4
using the function: $(t, (1-x^{\frac{2}{3}})^{\frac{3}{2}})$
thus i need to solve

$4\int\_0^1 \! \sqrt{(1-x^{\frac{2}{3}})^3} \, \mathrm{d}x. $

what would be the right direction? i have been trying substitution using sin() function as used for $1-x^2$ examples, but it doesnt help much

i'm sure there is a simple trick to get started here

thanks for any hint on this