Complex 360!

Algebra Level 5

\[ \large (x+1)(x+2)(x+3)^2 (x+4)(x+5) - 360 \]

If the non-real complex roots of the expression above can be expressed as

\[\pm \left( \sqrt { \sqrt { x } -y } \right) -z\pm \left( \sqrt { \sqrt { x } +y } \right) i \, \]

where \(x, y,\) and \(z\) are integers, find the value of \(x+y+z\).

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