This paper considers a mobile edge computing-enabled cell-free massive MIMO wireless network. An optimization problem for the joint allocation of uplink powers and remote computational resources is formulated, aimed at minimizing the total uplink power consumption under latency constraints, while simultaneously also maximizing the minimum SE throughout the network. Since the considered problem is non-convex, an iterative algorithm based on sequential convex programming is devised. A detailed performance comparison between the proposed distributed architecture and its co-located counterpart, based on a multi-cell massive MIMO deployment, is provided. Numerical results reveal the natural suitability of cell-free massive MIMO in supporting computation-offloading applications, with benefits over users' transmit power and energy consumption, the offloading latency experienced, and the total amount of allocated remote computational resources.