We demonstrate that thin films of randomly oriented metallic single-walled carbon nanotubes possess optical resonances with significant dispersion. The resonances are observed in the Kretschmann configuration as minima in reflection spectra close to 400 nm and 700 nm wavelengths. The dispersions are visible only when the material is excited with s-polarized light, and most prominent in layers with thickness near 100 nm. We conclude that magnetic plasmon polaritons arising from intertube interactions are a likely explanation. Closeness of the M11 and M22 transition energies to the observed resonances points to a possible coupling with excitons.