Recently, the cooperative effects due to the resonant dipole-dipole interactions (RDDIs) in dense cold atomic media have drawn significant attention. Cooperative Lamb shift, superradiance or subradiance have been observed in the fluorescence or absorption spectra in a two-level cycling transition. One may wondering what is the role of the RDDI in electromagnetically induced transparency (EIT) and slow light in a three-level L–type system. We report our experimental evidence of the effect due to RDDI in EIT and slow light experiment. Specifically, a spectral broadening effect is observed at high optical depths which may degrade the storage efficiency of an EIT-based optical memory. We present a theory which incorporates the RDDI in the optical Bloch equation to explain our experiment. We also discuss the possibility of turning the cooperative effect into help in an EIT-based optical memory.