Hyperfine-structure constants for the 6s2S1/2 and 6p2P1/2 atomic states of the Iπ=11/2- gold isomers Aum177,191,193,195 have been measured at CERN-ISOLDE, using the in-source laser resonance-ionization spectroscopy technique. From the measured hyperfine constants the differences between hyperfine anomalies for these atomic states have been deduced. These differential hyperfine anomaly values have been used to determine the 6s-state hyperfine anomaly relative to the stable Au197 with advanced atomic calculations. Magnetic dipole moments for the gold isomers in question have been deduced, taking into account the corresponding relative hyperfine-anomaly values. It has been shown that the commonly used prescription for the extraction of the magnetic moment values for the gold isotopes should be reconsidered. The magnetic moments calculated by this prescription have been reevaluated by properly accounting for the hyperfine anomaly, which is as large as 10% for several gold isotopes.