# 432 Is Special

Let $$S$$ be the set of rational numbers $$x$$ such that $$x^3-432$$ is the square of a rational number.

If $$S$$ is infinite, enter $$-1$$. If $$S$$ is finite, enter the sum of the elements of $$S.$$

Here is a very helpful hint:
If $$y^2=x^3-432,$$ let $$u = \dfrac{36-y}{6x}, \, v = \dfrac{36+y}{6x}$$. What is $$u^3+v^3$$?

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