Context. TOI-1055 is a Sun-like star known to host a transiting Neptune-sized planet on a 17.5-day orbit (TOI-1055 b). Radial velocity (RV) analyses carried out by two independent groups using nearly the same set of HARPS spectra have provided measurements of planetary masses that differ by ∼2σ. Aims. Our aim in this work is to solve the inconsistency in the published planetary masses by significantly extending the set of HARPS RV measurements and employing a new analysis tool that is able to account and correct for stellar activity. Our further aim was to improve the precision on measurements of the planetary radius by observing two transits of the planet with the CHEOPS space telescope. Methods. We fit a skew normal function to each cross correlation function extracted from the HARPS spectra to obtain RV measurements and hyperparameters to be used for the detrending. We evaluated the correlation changes of the hyperparameters along the RV time series using the breakpoint technique. We performed a joint photometric and RV analysis using a Markov chain Monte Carlo scheme to simultaneously detrend the light curves and the RV time series. Results. We firmly detected the Keplerian signal of TOI-1055 b, deriving a planetary mass of M_b = 20.4_−2.5^+2.6 M_⊕ (∼12%). This value is in agreement with one of the two estimates in the literature, but it is significantly more precise. Thanks to the TESS transit light curves combined with exquisite CHEOPS photometry, we also derived a planetary radius of R_b = 3.490_−0.064^+0.070 R_⊕ (∼1.9%). Our mass and radius measurements imply a mean density of ρ_b = 2.65_−0.35^+0.37 g cm⁻³ (∼14%). We further inferred the planetary structure and found that TOI-1055 b is very likely to host a substantial gas envelope with a mass of 0.41_−0.20^+0.34 M_⊕ and a thickness of 1.05_−0.29^+0.30 R_⊕. Conclusions. Our RV extraction combined with the breakpoint technique has played a key role in the optimal removal of stellar activity from the HARPS time series, enabling us to solve the tension in the planetary mass values published so far for TOI-1055 b.