Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.