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Coherent perfect absorption (CPA) is an interferometric effect that guarantees full absorption in a lossy layer independently of its intrinsic losses. To date, it has been observed only at a single wavelength or narrow bandwidths, whereupon wavelength-dependent absorption can be ignored. Here we produce CPA over a bandwidth of ~ 60 nm in a 2-um-thick polymer film with a low-doping concentration of an organic laser dye. A planar cavity is designed with a spectral `dip' to accommodate the dye resonant linewidth, and CPA is thus achieved even at its absorption edges. This approach allows realizing strong absorption in laser dyes - and resonant materials in general - independently of the intrinsic absorption levels, with a at spectral profile and without suffering absorption quenching due to high doping levels.