The low-frequency part of the magnetic resonance spectrum of the hexagonal six-sublattice quasi-one-dimensional antiferromagnet CsMnBr3 at temperatures which are low compared with T N =8.3 K is investigated experimentally. A temperature-dependent gap Δ(T) is found in the spectrum ω e (H) of the lower AFMR branch; this gap is due to the hyperfine interaction of the nuclear spins with the electronic spins of the (55Mn)2+ ions. The spectrum of the low-lying resonance frequencies of such a system is calculated taking this interaction into acount in the approximation of fluctuationless spin hydrodynamics for the electronic branch of the oscillations. The computational results are in good qualitative and satisfactory quantitative agreement with experiment.