Given the values $\displaystyle {1},{2},{4}$, find all numbers listed that are solution of the equation. (Careful, there might be more than one that work!) If you find several solutions, separate them with a comma. If none of the given numbers work, just enter DNE for 'does not exist'.

$\displaystyle {x}^{{3}}-{11}{x}^{{2}}+{x}-{4}=-{6}{x}^{{2}}-{3}{x}-{4}$