Optical random access memories (RAMs) have been conceived as high-bandwidth alternatives of their electronic counterparts, raising expectations for ultra-fast operation that can resolve the ns-long electronic RAM access bottleneck. However, experimentally demonstrated optical RAMs have been limited to up to 5 GHz only, failing to validate the speed advantages over electronics. In this Letter, we demonstrate the first all-optical RAM cell that performs both Write and Read functionalities at 10 Gb/s, reporting on a 100% speed increase compared to state-of-the-art optical RAM demonstrations. To achieve this, the proposed RAM cell deploys a monolithically integrated InP optical Flip-Flop and a Semiconductor optical amplifier-Mach-Zehnder Interferometer (SOA-MZI) On/Off switch configured to operate as a strongly saturated differentially-biased access gate. Error-free operation is demonstrated at 10 Gb/s for both Write and Read operations with 6.2 dB and 0.4 dB power, respectively, achieving the fastest reported RAM cell functionalities.