Tidal dissipation in late-type stars is presently poorly understood and the study of planetary systems hosting hot Jupiters can provide new observational constraints to test proposed theories. We focus on systems with F-type main-sequence stars and find that the recently discovered system CoRoT-11 is presently the best suited for such a kind of investigation. A classic constant tidal lag model is applied to reproduce the evolution of the system from a plausible nearly synchronous state on the ZAMS to the present state, thus putting constraints on the average modified tidal quality factor of its F6V star. Initial conditions with the stellar rotation period longer than the orbital period of the planet can be excluded on the basis of the presently observed state in which the star spins faster than the planet orbit. It is found that is approximately between 4.0E+06 and 2.0E+07 if the system started its evolution on the ZAMS close to synchronization with an uncertainty related to the constant tidal lag hypothesis and the estimated stellar magnetic braking within a factor of about 5-6. Moreover, we discuss how the present value of Q'_s can be measured by a timing of the mid-epoch and duration of the transits as well as of the planetary eclipses to be observed in the infrared with an accuracy of about 0.5-1 s over a time baseline of about 25 yr. CoRoT-11 is an highly interesting system potentially allowing us a direct measure of the tidal dissipation in an F-type star as well as the detection of the precession of the orbital plane of the planet that provides us with an accurate upper limit for the obliquity of the stellar equator. If the planetary orbit has a significant eccentricity (e>0.05), it will be possible to detect also the precession of the line of the apsides and derive information on the Love number of the planet and its tidal quality factor. ; Comment: 10 pages, 5 figures, 1 table, accepted by Astronomy & Astrophysics