\(\left(x+1\right)^3+\left(x-1\right)^3=2x^3\)
\(\left(x^3+3x^2+3x+1\right)+\left(x^3-3x^2+3x-1\right)=2x^3\)
\(\left(x^3+x^3\right)+\left(3x^2-3x^2\right)+\left(3x+3x\right)+\left(1-1\right)=2x^3\)
\(2x^3+6x=2x^3\)
\(2x^3+6x-2x^3=2x^3-2x^3\)
\(6x=0\\ x=0\)