Inspired from dev sharma's note

Algebra Level 3

If \({x}^6 = {y}^4 + 18\) and \({y}^6 = {x}^4 + 18\) such that (x,y) are real numbers. Then find the sum of squares of all possible values of x and y.
Details and assumptions

if x = 4 , y = 2 and x = 4 , y = 3 then the answer should be entered as \({4}^2 + {3}^2 + {2}^2\) and 4 is not included twice.

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