Will you cube each term?

Algebra Level 4

(x2+x2)3+(2x2x1)3=27(x21)3\large (x^{2} + x-2)^3 + (2x^2 - x -1)^{3} = 27(x^2-1)^{3}

Find the sum of all distinct real roots of xx satisfying the above equation.


Source: Regional Mathematics Olympiad, India.
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