We discuss the first results of the Fermi-GBM all-sky search for X-ray bursts. The very large field of view and X-ray response of the Fermi-GBM make it a unique instrument to study rare, bright and short-lived X-ray bursts. We are performing a systematic search that exploits such capabilities. We present results on long/intermediate type I X-ray bursts, an unusual kind of thermonuclear bursts from accreting neutron stars, and show how Fermi-GBM is giving, for the first time, robust measurements of their recurrence time.