The miscible displacement of a shear-thinning fluid by another of same rheological properties is studied experimentally in a transparent fracture by an optical technique imaging relative concentration distributions. The fracture walls have complementary self-affine geometries and are shifted laterally in the direction perpendicular to the mean flow velocity {\bf U} : the flow field is strongly channelized and macro dispersion controls the front structure for Péclet numbers above a few units. The global front width increases then linearly with time and reflects the velocity distribution between the different channels. In contrast, at the local scale, front spreading is similar to Taylor dispersion between plane parallel surfaces. Both dispersion mechanisms depend strongly on the fluid rheology which shifts from Newtonian to shear-thinning when the flow rate increases. In the latter domain, increasing the concentration enhances the global front width but reduces both Taylor dispersion (due to the flattening of the velocity profile in the gap of the fracture) and the size of medium scale front structures.