The coherent spin dynamics of resident electrons and holes in an isotopically purified ZnSe/(Zn,Mg)Se single quantum well is investigated in different regimes, requiring corresponding adaption of the applied time-resolved pump-probe Kerr rotation technique. The purification of the Zn and Se atom species in the crystal to the isotopes with zero nuclear spin is expected to lead to an extension of the spin dephasing times of resident carriers, due to the suppression of their interaction with the nuclear spins. Indeed, we find no indication of carrier-nuclear interaction in this sample and link the observed carrier spin relaxation to the spin-orbit interaction. Theoretical considerations support the experimental results.