We study arrays of silver split-ring resonators operating at around 1.5-µm wavelength coupled to an MBE-grown single 12.7-nm thin InGaAs quantum well separated only 4.8 nm from the wafer surface. The samples are held at liquid-helium temperature and are pumped by intense femtosecond optical pulses at 0.81-µm center wavelength in a pump-probe geometry. We observe much larger relative transmittance changes (up to about 8%) on the split-ring-resonator arrays as compared to the bare quantum well (not more than 1-2%). We also observe a much more rapid temporal decay component of the differential transmittance signal of 15 ps for the case of split-ring resonators coupled to the quantum well compared to the case of the bare quantum well, where we find about 0.7 ns. These observations are ascribed to the evanescent coupling of the split-ring resonators to the quantum-well gain. All experimental results are compared with a recently introduced analytical toy model that accounts for this evanescent coupling, leading to excellent overall qualitative agreement.