Most machine learning force fields (MLFFs) use local or semi-local features to predict energies of atomic configurations. While a variety of approaches were proposed to account for the influence of long-range electrostatics, practitioners are forced to truncate known DFT dispersion corrections at short distances to avoid expensive neighbour list computations. Although such computations are routine in DFT due to an even greater cost of the underlying exchange-correlation functional, the remarkable evaluation speed of MLFFs presents a challenge in the modelling of long-range dispersion. We develop a mathematical framework which makes it possible to evaluate the DFT-D3 dispersion correction using fast summation techniques at a fraction of the cost of direct summation. Our reference implementation can be easily integrated with any short-range MLFF and does not require any supplementary training. We demonstrate the convergence of our method to chemical accuracy on a range of systems and perform molecular dynamics simulations that illustrate the sensitivity of mesoscale and thermodynamic properties such as water density and enthalpy of vaporization to long-range dispersion. In addition, we argue that our methodology in its maximal configuration represents a truly converged dispersion correction that should be used for DFT calculations in place of the current approaches that compute large neighbour lists. More broadly, our mathematical framework creates opportunities to develop novel dispersion corrections and to create machine learning architectures that learn from non-local exchange-correlation functionals.