The discovery of chiral helical magnetism (CHM) in Cr_1/3NbS₂ and the stabilization of a chiral soliton lattice (CSL) has attracted considerable interest in view of their potential technological applications. However, there is an ongoing debate regarding whether the sister compound, Mn_1/3NbS₂, which shares the same crystal structure, exhibits similar nontrivial properties, which rely on the stabilization of the lack of inversion symmetry at the magnetic ion. In this study, we conduct a comprehensive investigation of the magnetically ordered states of both compounds, using ⁵³Cr, ⁵⁵Mn and ⁹³Nb nuclear magnetic resonance. Our results, supported by density functional calculations, detect in a high quality single crystal of Cr_1/3NbS₂ all the signatures of the monoaxial CHM in a magnetic field, identifying it as a textbook NMR case. The detailed understanding of this prototypic behavior provides a reference for Mn_1/3NbS₂. Despite the much larger density of specific defects in this second single crystal, we confirm the presence of a CHM phase in the Mn compound, characterized by a very large critical field for the forced ferromagnetic phase (~ 10 T for H || c).