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The electron spin dynamics is investigated by the time-resolved Kerr rotation technique in a pair of special GaAs/AlGaAs asymmetric quantum well samples grown on (111)-oriented substrates, whose structures are the same except for their opposite directions of potential asymmetry. A large difference of spin lifetimes between the two samples is observed at low temperature. This difference is interpreted in terms of a cancellation effect between the Dresselhaus spin-splitting term in the conduction band and another term induced by interface inversion asymmetry. The deviation decreases with the increasing temperature, and almost disappears when T > 100 K because the cubic Dresselhaus term becomes more important.