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We study the cosmological predictions of the dark D-brane model, in which dark matter resides on a D-brane moving in a higher-dimensional space. By construction, dark matter interacts only gravitationally with the standard model sector in this framework. The dark energy scalar field is associated with the position of the D-brane, and its dynamics is encoded in a Dirac-Born-Infeld action. On the other hand, dark matter is identified with matter on the D-brane, that naturally couples to dark energy \textit{via} a disformal coupling. We analyse the numerical evolution of the cosmological background, highlighting the fact that there are two regimes of interest: one, in which the coupling is positive throughout; and another, in which the coupling is negative at the present. In the latter, there is the enticing possibility of having scenarios in which the coupling is positive for a significant part of the evolution, before decreasing towards negative values. In both cases, the coupling is very small at early times, and only starts to grow during the late matter dominated era. We also derive the equations for the linear cosmological perturbations, an expression for the effective time-dependent gravitational coupling between dark matter particles and present the numerical results for the CMB anisotropy and matter power spectra. This allows for a direct comparison of the predictions for the growth of large scale structure with other disformal quintessence models.