Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) remains difficult due to an inherent degeneracy between fibre dispersion and diffusion anisotropy. This means that estimates of fibre dispersion rely on strong assumptions, such as constant anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. In simulations we show that the bias in fibre dispersion is greatly reduced (~5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data even if overly simplistic tissue assumptions are used. In in vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1.5 ms/$\mu$m, increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions made of the tissue microstructure.