If this has rational roots (and so nice factors) by the rational root theorem the roots are amoung the factors of 24, so try +/11, +/-2, +/-3, +/-4, +/-6, +/-8, +/-12. If none of these are roots then it has no rational roots and so no linear factors with integer coefficients.
(As it happens none of these are roots and so this cubic has no nice factors, but it does have exactly one real root)
You can find the root algebraicaly by using the Cardano-Tartaglia cubic formula, though you will probably be better off solving for the real root numerically
CB