The effect of coupling to the projectile breakup channel on 11Li elastic scattering from 12C at 57.9 MeV/nucleon and 28Si at 29 MeV/nucleon is investigated. Correlated 11Li wave functions based on Faddeev three-body models are used within a four-body ( 9Li+n+n+A ) Glauber scattering model. The single-folded potential for 11Li is calculated and used to isolate the part of the scattering amplitude from coupling to breakup states. It is found that the breakup has a large effect on the elastic cross sections and that higher-order breakup terms, such as that responsible for continuum-continuum coupling, are important. The dynamic polarisation potential representation of the breakup effect is calculated and found to be strongly absorptive and with a significant repulsive real part in the far surface region, which is qualitatively similar to that found in 12C scattering.