  Small rocky planets seem to be very abundant around low-mass M-type stars.
Their actual planetary population is however not yet precisely understood.
Currently several surveys aim to expand the statistics with intensive detection
campaigns, both photometric and spectroscopic. We analyse 106 spectroscopic
HARPS-N observations of the active M0-type star GJ 685 taken over the past five
years. We combine these data with photometric measurements from different
observatories to accurately model the stellar rotation and disentangle its
signals from genuine Doppler planetary signals in the RV data. We run an MCMC
analysis on the RV and activity indexes time series to model the planetary and
stellar signals present in the data, applying Gaussian Process regression
technique to deal with the stellar activity signals. We identify three periodic
signals in the RV time series, with periods of 9, 24, and 18 d. Combining the
analyses of the photometry of the star with the activity indexes derived from
the HARPS-N spectra, we identify the 18 d and 9 d signals as activity-related,
corresponding to the stellar rotation period and its first harmonic
respectively. The 24 d signals shows no relations with any activity proxy, so
we identify it as a genuine planetary signal. We find the best-fit model
describing the Doppler signal of the newly-found planet, GJ 685\,b,
corresponding to an orbital period $P_b = 24.160^{+0.061}_{-0.047}$ d and a
minimum mass $M_P \sin i = 9.0^{+1.7}_{-1.8}$ M$_\oplus$. We also study a
sample of 70 RV-detected M-dwarf planets, and present new statistical evidence
of a difference in mass distribution between the populations of single- and
multi-planet systems, which can shed new light on the formation mechanisms of
low-mass planets around late-type stars.
