Searches for CP violation in the decays D(s)+→ηπ+ and D(s)+→η′π+ are performed using pp collision data corresponding to 6 fb−1 of integrated luminosity collected by the LHCb experiment. The calibration channels D(s)+→ϕπ+ are used to remove production and detection asymmetries. The resulting CP-violating asymmetries areACP=(D+→ηπ+)=(0.34±0.66±0.16±0.05)%,ACP=(Ds+→ηπ+)=(0.32±0.51±0.12)%,ACP=(D+→η′π+)=(0.49±0.18±0.06±0.05)%,ACP=(Ds+→η′π+)=(0.01±0.12±0.08)%, where the first uncertainty is statistical, the second is systematic and the third, relevant for the D+ channels, is due to the uncertainty on ACP= (D+→ ϕπ+). These measurements, currently the most precise for three of the four channels considered, are consistent with the absence of CP violation. A combination of these results with previous LHCb measurements is presented. [Figure not available: see fulltext.].