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Aims. We have investigated the lensing event KMT-2024-BLG-0404. The light curve of the event exhibited a complex structure with multiple distinct features, including two prominent caustic spikes, two cusp bumps, and a brief discontinuous feature between the caustic spikes. While a binary-lens model captured the general anomaly pattern, it could not account for a discontinuous anomaly feature between the two caustic spikes. Methods. To explore the origin of the unexplained feature, we conducted more advanced modeling beyond the standard binary-lens framework. This investigation demonstrated that the previously unexplained anomaly was resolved by introducing an additional lens component with planetary mass. Results. The estimated masses of the lens components areM_p= 17.3_−8.8^+25.5M_Efor the planet, andM_h,A= 0.090_−0.046^+0.133M_⊙andM_h,B= 0.026_−0.013^+0.038M_⊙for the binary host stars. Based on these mass estimates, the lens system is identified as a planetary system where a Uranus-mass planet orbits a binary consisting of a late M dwarf and a brown dwarf. The distance to the planetary system is estimated to beD_L= 7.21_−0.97^+0.93kpc, with an 82% probability that it resides in the Galactic bulge. This discovery represents the ninth planetary system found through microlensing with a planet orbiting a binary host. Notably, it is the first case in which the host consists of both a star and a brown dwarf.