Velocity estimation plays a central role in driverless vehicles, but standard and affordable methods struggle to cope with extreme scenarios like aggressive maneuvers due to the presence of high sideslip. To solve this, autonomous race cars are usually equipped with expensive external velocity sensors. In this paper, we present an end-to-end recurrent neural network that takes available raw sensors as input (IMU, wheel odometry, and motor currents) and outputs velocity estimates. The results are compared to two state-of-the-art Kalman filters, which respectively include and exclude expensive velocity sensors. All methods have been extensively tested on a formula student driverless race car with very high sideslip (10{\deg} at the rear axle) and slip ratio (~20%), operating close to the limits of handling. The proposed network is able to estimate lateral velocity up to 15x better than the Kalman filter with the equivalent sensor input and matches (0.06 m/s RMSE) the Kalman filter with the expensive velocity sensor setup.