Aims. We present the results of the combined photometric and spectroscopic analysis of a bright (V = 9.14), close (d = 31 pc), late-type detached eclipsing binary, AK Fornacis. This P = 3.981 d system has not been previously recognised as a double-lined spectroscopic binary, and this is the first full physical model of this unique target. Methods. With the FEROS, CORALIE, and HARPS spectrographs, we collected a number of high-resolution spectra to calculate radial velocities of both components of the binary. Measurements were done with our own disentangling procedure and the TODCOR technique, and were later combined with the photometry from the ASAS and SuperWASP archives. We also performed an atmospheric analysis of the component spectra with the Spectroscopy Made Easy package. Results. Our analysis shows that AK For consists of two active, cool dwarfs having masses of M1 = 0.6958 ± 0.0010 and M2 = 0.6355 ± 0.0007 M⊙ and radii of R 1 = 0.687 ± 0.020 and R2 = 0.609 ± 0.016 R⊙, respectively, which are slightly less metal-abundant than the Sun. Parameters of both components are well reproduced by the models. Conclusions. AK For is the brightest system among the known eclipsing binaries with K-or M-type stars. Its orbital period is one of the longest, and its rotational velocities is one of the lowest, which allows us to obtain very precise radial velocity measurements. The precision in physical parameters that we obtained places AK For among the binaries with the best mass measurements in the literature. It also fills the gap in our knowledge of stars in the range of 0.5-0.8 M⊙ and between short and long-period systems. All this makes AK For a unique benchmark for understanding the properties of low-mass stars. © 2014 ESO.