Školjka

%V0 Let $m \neq 0$ be an integer. Find all polynomials $P(x)$ with real coefficients such that $$ (x^3 - m x^2 + 1)P(x + 1) + (x^3 + m x^2 + 1)P(x - 1) = 2(x^3 - m x + 1)P(x) $$ for all real numbers $x$.