We present a detailed characterization of the Kepler-411 system (KOI 1781). This system was previously known to host two transiting planets: one with a period of 3 days (R = 2.4 R-circle plus; Kepler-411b) and one with a period of 7.8 days (R = 4.4 R-circle plus; Kepler-411c), as well as a transiting planetary candidate with a 58-day period (R = 3.3 R-circle plus; KOI 1781.03) from Kepler photometry. Here, we combine Kepler photometry data and new transit timing variation (TTV) measurements from all the Kepler quarters with previous adaptive-optics imaging results, and dynamical simulations, in order to constrain the properties of the Kepler-411 system. From our analysis, we obtain masses of 25.6 +/- 2.6 M-circle plus for Kepler-411b and 26.4 +/- 5.9 M-circle plus for Kepler-411c, and we confirm the planetary nature of KOI 1781.03 with a mass of 15.2 +/- 5.1 M-circle plus , hence the name Kepler-411d. Furthermore, by assuming near-coplanarity of the system (mutual inclination below 30 degrees), we discover a nontransiting planet, Kepler-411e, with a mass of 10.8 +/- 1.1 M-circle plus on a 31.5-day orbit, which has a strong dynamical interaction with Kepler-411d. With densities of 1.71 +/- 0.39 g cm(-3) and 2.32 +/- 0.83 g cm(-3), both Kepler-411c and Kepler-411d belong to the group of planets with a massive core and a significant fraction of volatiles. Although Kepler-411b has a sub-Neptune size, it belongs to the group of rocky planets.