B737-800 FLT CREW EXPERIENCED A FUEL IMBALANCE ENROUTE. UNABLE TO BALANCE THE FUEL; THE FLT CREW DECLARED AN EMER AND DIVERTED.

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WE WERE LEVEL AT FL360 ON A RETURN LEG TO LAX. A LITTLE OVER 1 HR INTO THE FLT; THE CAPT OPENED THE FUEL XFEED VALVE AND TURNED OFF A CTR TANK FUEL BOOST PUMP IN ACCORDANCE WITH OUR PROC WITH LESS THAN 2000 LBS REMAINING IN THE CTR TANK. SEVERAL MINS AFTER THAT; WE GOT A FUEL IMBALANCE WARNING LIGHT. THE IMBALANCE WAS AROUND 1100 LBS. THE CAPT REFED THE QRH AND STARTED THE REBALANCING PROC. THAT SEEMED TO BE WORKING SOMEWHAT; HOWEVER; THE L SIDE TANK (WHICH WAS THE LOW SIDE) WAS STILL FEEDING WHEN IT SHOULD NOT HAVE BEEN. THIS PUZZLED US AND I STARTED TRYING TO CALL OUR COMPANY MAINT ON VHF WITH NO LUCK. THE IMBALANCE WAS IMPROVING THOUGH; AND HAD DECREASED TO AROUND 900 LBS. WHEN THE CAPT STARTED THE REBALANCING PROC; THE CTR TANK WHICH HAD 1300 LBS REMAINING STOPPED FEEDING AS EXPECTED. WE DECIDED TO TURN THOSE CTR PUMPS BACK ON TO BURN THAT FUEL WHICH CAUSED THE WING TANKS TO STOP FEEDING AS EXPECTED. SO WE BURNED THE REMAINING CTR FUEL AND THEN WENT BACK TO TRYING TO REBALANCE THE WING TANKS WHICH STILL HAD ABOUT A 900 LB IMBALANCE. I CONTINUED TO TRY AND CALL OUR COMPANY ON BOTH VHF AND HF WITH NO LUCK. NOW WITH THE REBALANCING IN EFFECT; THE IMBALANCE STARTED GETTING WORSE WITH THE L SIDE FEEDING AT LEAST TWICE AS FAST AS THE R SIDE WHICH WAS THE HIGH SIDE. WE ALSO DISCOVERED THAT THE XFEED LIGHT ON THE FUEL PANEL WAS INOP EVEN AFTER WE CHANGED THE BULBS. WE STARTED TO THINK WE EITHER HAD A POSSIBLE LEAK OR TRAPPED FUEL IN THE R TANK. WE STARTED TO THINK ABOUT POSSIBLE DIVERT FIELDS AND REALIZED THE FIELD AT ZZZ1 WAS ABOUT 40 MI AWAY WHILE ZZZ2 IN THE UNITED STATES WAS ABOUT 250 MI AWAY. I SENT BOTH OUR DISPATCHER AND MAINT AN ACARS MESSAGE ABOUT OUR PROB AND THEY BOTH ACKNOWLEDGED WITH GENERIC RESPONSES. THE IMBALANCE HAD NOW GOTTEN BACK TO ABOUT 1100 LBS AND WAS CONTINUING TO WORSEN. WE THEN DECIDED TO DIVERT INTO ZZZ1 BECAUSE WE WEREN'T SURE WE HAD ENOUGH USABLE FUEL TO GET US TO ZZZ2 OR HOW LARGE THE IMBALANCE WOULD BE WHEN WE GOT THERE. DURING THE DSCNT EITHER MAINT OR THE DISPATCHER SENT US AN ACARS WITH A POSSIBLE SOLUTION TO THE PROB; HOWEVER; WE WERE WELL INTO THE DIVERT; DID NOT TAKE TIME TO INVESTIGATE FURTHER. ONCE ON THE GND AT ZZZ1; THE CAPT TALKED WITH MAINT ON THE PHONE AND THEY DIRECTED US TO CHK THE FUEL XFEED CIRCUIT BREAKER BEHIND THE FO'S SEAT. WE FOUND THE BREAKER WAS OUT AND CONTRACT MAINT WAS ABLE TO COME OUT AND RESET THE BREAKER AND RETURN THE ACFT TO SVC.