# 432 Is Special

**Number Theory**Level 5

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 \( u^3+v^3\)?