Bright thinking!

$x^3 - x^2 - x = 37^3 - 37^2 - 37 \implies x^3 - x^2 - x - 49247 = 0$ . Assume $f(x) = x^3 - x^2 - x - 49247$

$\begin{aligned} x^3 - x^2 - x - 49247& = 0 \\ \Rightarrow x^3 - 37x^2 + 36x^2 -1332x+1331x-49247 & = 0 \\ \Rightarrow x^2(x - 37) + 36x(x -37) +1331(x-37) & = 0 \\ \Rightarrow (x - 37)(x^2 + 36 x + 1331) & = 0 \\ \Rightarrow x^2 + 36x + 1331 & = 0 \\ \end{aligned}$

By the quadratic equation formula, we get $x = -18 \pm i\sqrt{1007}$ . Hence $x = 37$ is not unique.

Note: $x - 37$ is a factor of $f(x)$ because $f(37) =0$