Making An Equation Complex Doesn't Make It Harder

Algebra Level 4

How many ordered pairs of real numbers \( (x, y) \) are there such that

\[ 1 = (y-x) ( x^2 + y^2) = (2xy + \frac{ 3} { \sqrt[3]{2} })(x^2+y^2)^2 ? \]

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