It looks difficult , but not that difficult

Calculus Level 4

If (x-y)f(x+y) - (x+y)f(x-y) = 4xy(x^{2} - y^{2}) , find the area common to both the curves [f(y)]^{\frac{2}{3}} + [f(x)]^{\frac{1}{3}} = 0 and [f(y)]^{\frac{2}{3}} + [f(x)]^{\frac{2}{3}} = 12

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