We investigate the influence of adding C-60 nanoparticles on the dielectric relaxation spectra of both unentangled and entangled polyisoprene (PIP). Relaxation modes corresponding to both the segmental and chain relaxation were analyzed over a broad temperature and frequency range. Regardless of whether the chains were entangled or not, both relaxation processes slowed down with the addition of C-60, reflecting an increase of the nanocomposite glass transition temperature. However, C-60 affects the segmental relaxation more strongly than the large-scale chain relaxation, both in terms of the relaxation time and strength, suggesting that the effect of the nanoparticles on the polymer dynamics is scale dependent. This effect is attributed to a difference in packing frustration at different length scales, a phenomenon also relevant to understanding the difference between the temperature dependence of the segmental and chain relaxation processes in neat polymer materials. Further evidence of this scale dependence is indicated by the observation that the secondary relaxation time of the high molecular mass PIP decreases with an addition of C-60. These observations indicate that C-60 has an effect opposite to antiplasticizing additives that slow down the secondary relaxation (stiffening the material) in the glass state, while at the same time reducing the alpha relaxation time associated with cooperative segmental and chain motions. Recent incoherent neutron scattering measurements have indicated that C-60 can have a similar effect on polystyrene.