B757 LEFT ENG FAILED DURING CRUISE. EMER WAS DECLARED AND FLT DIVERTED TO NEAREST SUITABLE ARPT.

Narrative

AT OUR CRUISE ALT FL380; WE WERE CLRED DIRECT TO ZUN; A POINT ON OUR ARR. AS WE PASSED ABEAM XXX; WE COMPLETED AND SENT A POS RPT. SEVERAL MINS LATER; THE FO AND I BOTH OBSERVED THE L (#1) ENG FAILURE. THE ENG SHUT DOWN WITH NO ABNORMAL SOUNDS. WE RAN THE QRH ENG FAILURE CHKLIST. I DECLARED AN EMER; AND COORD WITH ATC FOR A DSCNT OUT OF FL380. WE EVALUATED OUR AVAILABLE OPTIONS AND DECIDED TO LAND AT ZZZ WHICH WAS THE NEAREST SUITABLE ARPT. ATC ASSISTED IN OUR DIRECT ROUTING TO ZZZ. IN ACCORDANCE WITH THE ABNORMAL CHKLIST FOR ENG FAILURE; THE FO ATTEMPTED TO START THE APU. THE APU DID NOT START AND THE 'APU FAULT' LIGHT ILLUMINATED. WE RAN THE 'APU FAULT' QRH CHKLIST; AND THE APU STARTED ON THE SECOND ATTEMPT. WITH NO ABNORMAL INDICATIONS ON THE SHUTDOWN ENG; VARIOUS DEGREES OF WX AT ALL NEARBY ARPTS; AND THE APU FAULT CONDITION; WE ELECTED TO PERFORM THE ENG INFLT START CHKLIST. AFTER 30 SECONDS; THE RESTART WAS UNSUCCESSFUL (0 FUEL FLOW). WE NOTIFIED THE DISPATCHER VIA ACARS; SPOKE VIA INTERCOM TO THE FLT ATTENDANTS; AND OVER THE PA TO THE PAX. OVERWT LNDG CONSIDERATIONS WERE DISCUSSED. IT APPEARED WE WOULD BE ABOUT 1000 LBS OVER MAX LNDG WT AT TOUCHDOWN. A SINGLE ENG ILS APCH AND LNDG WAS CONDUCTED TO RWY 6 AND WAS UNEVENTFUL. COORD WITH TWR AND FIRE/EMER RESPONSE PERSONNEL WAS APPARENT. WE TAXIED UNDER OUR OWN PWR AND WERE PARKED NEAR THE GATE.