Sum of Squares

The number $648000$ can be represented in two ways as the sum of two perfect squares, as follows:

${ a }^{ 2 }+{ b }^{ 2 }=648000$ and ${ c }^{ 2 }+{ d }^{ 2 }=648000$ , such that $a\neq b\neq c\neq d$ , and $a, b, c, d$ are positive integers.

Find $a+b+c+d$