B767-300 LEADING EDGE ASYMMETRY OCCURRED DURING TKOF AND STICK SHAKER ACTIVATED. FLT CONTINUED TKOF AND DECLARED EMER. FUEL WAS DUMPED FOR A RETURN TO DEP ARPT.

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FLT HAD BEEN DELAYED DUE TO MAINT PROBS THE NIGHT BEFORE. THE NEXT DAY THE FLT PUSHED BACK FROM THE GATE AND ON ENG START WE GOT EICAS OF A L ENG OIL FILTER AND THEN A STATUS MESSAGE. CHKLIST WAS FOLLOWED AND DISPATCH AND MAINT CTL CONTACTED. RETURNED TO THE GATE AND MAINT CHANGED FILTER. FLT THEN DEPARTED. AT TKOF ROLL ROTATION GOT A STICK SHAKER AND EICAS WARNING OF A LEADING EDGE SLAT ASYMMETRY. CONTINUED TKOF; MAINTAINED A SPD LESS THAN THE FLAPS 5 DEGS THAT WAS SELECTED FOR TKOF. THE APPROPRIATE CHKLIST WAS USED AND AFTER FOLLOWING THE CHKLIST; TALKING WITH DISPATCH; AND MAINT CTL; IT WAS DETERMINED THAT RETURNING TO ZZZ WAS THE ONLY OPTION. COORD WAS DONE WITH APCH TO DUMP FUEL. FUEL WAS DUMPED AT 5000 FT. APPROX 50000 LBS WAS DUMPED. DURING THIS TIME; COORD WAS DONE WITH DISPATCH FOR LNDG DATA; EMER EQUIP AND OTHER ITEMS. ALSO DURING FUEL DUMP 'NO COOLING' LIGHT CAME ON THE OVERHEAD; AND CHKLIST WAS FOLLOWED FOR THIS ITEM AND MAINT CTL WAS CONSULTED. THE RELIEF PLT FOUND IN THE FLT MANUAL WHERE THIS SYS WAS ARMED DURING FUEL DUMPING BUT WAS HOPEFULLY NOT TO COME ON. LIGHT DID COME ON AND DURING THIS TIME WE HAD A L FMC FAILURE. DURING THE DUMPING OF FUEL; AN EMER WAS DECLARED AND A REQUEST WAS MADE FOR THE EQUIP TO STAND BY. BOTH APCH AND DISPATCH WERE NOTIFIED OF THIS REQUEST. DISPATCH WAS VERY HELPFUL MONITORING THE FREQ AND COORDINATING OUTSIDE ITEMS. REQUEST WAS MADE WITH APCH TO LAND INTO THE WIND. LEADING EDGE SLAT ASYMMETRY CHKLIST WAS FOLLOWED FOR THE FLAP EXTENSION PROC. WE WERE ABLE TO SUCCESSFULLY EXTEND TRAILING EDGE FLAPS WITH THE FLAP HANDLE AND DID NOT NEED TO USE THE ELECTRICAL ALTERNATE SYS. LNDG WAS COMMENCED AT A FLAPS 20 DEG SETTING WITH AN APCH SPD OF 180 KTS. AUTOBRAKES LEVEL 4 WAS SELECTED. THE RELIEF PLT CONSULTED THE ABNORMAL LNDG DISTANCE CHART AND CONFIRMED THIS DATA WITH THE DATA THAT WAS SENT BY DISPATCH. WE DETERMINED THAT A SUCCESSFUL LNDG COULD BE COMPLETED. THE ILS WAS FLOWN. TOUCHDOWN WAS NORMAL AND PLANE WAS BROUGHT TO A STOP BEFORE THE INTXN. THE ACFT EXITED THE RWY AND WE REQUESTED THE FIRE EQUIP TO INSPECT THE BRAKES. DURING THIS TIME THE BRAKE TEMP ON SEVERAL OF THE BRAKES WENT ABOVE 5 AND TWO WENT TO 9. WE THEN ASKED THE FIRE DEPT TO VISUAL WATCH OUR BRAKES. WE COORD OUR ENTRANCE TO THE GATE WITH MAINT AND THE RAMP. GND PERSONNEL WERE STANDING BY TO CHOCK THE AIRPLANE. APPROPRIATE MAINT CODES WERE SENT. AN OVERWT LNDG MAINT NOTE WAS SENT. THE WT OF THE LNDG WAS 347000 LBS.