DUE TO PLT CTLR CONFUSION WHILE ON LNDG ROLL AT LAX; ACR FLC DOES NOT MAKE TXWY EXIT; PROCEEDING TO NEXT TXWY EXIT; CAUSING GAR FOR FOREIGN ACR ON SHORT FINAL.

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WIND 080 DEGS AT 8 KTS. B757 (ACFT Y) ON TXWY M BTWN RWY 25L&R. WE (ACFT X) WERE LNDG; 5 MI BEHIND A HVY DC10 (ACFT W). A FOREIGN ACR (ACFT Z); 3 MI BEHIND US. THE DC10 WAS ON TXWY N BTWN RWY 25L&R. AFTER LNDG ON RWY 25L AND SLOWING THROUGH 100 KTS; ATC TOLD US TO 'EXIT TO THE R BEHIND COMPANY OR IF UNABLE MAKE A L AT TXWY A7.' WE STARTED THE R TURN AT TXWY M BEHIND THE B757. THEN; ATC SAID 'L TURN; L TURN ACR X.' SO WE STOPPED THE R TURN AND PROCEEDED STRAIGHT DOWN THE RWY; BECAUSE IT WAS TOO LATE TO MAKE THE L TURN AT TXWY A7. THE ACFT HAD TO BE TURNED IN A RAPID WAY WHICH WAS UNCOMFORTABLE. THE FOREIGN ACR HAD TO GO AROUND. THE CAPT SPOKE WITH THE TWR ON THE PHONE AND THEY SAID THEY ISSUED AN INSTRUCTION TO MAKE A HARD R TURN BEHIND COMPANY. WE NEVER HEARD THIS XMISSION. SOLUTION: LET THE PLTS EXIT THE RWY WHERE THEY FEEL IT IS SAFE. OUR INITIAL PLAN WAS TO TURN R BEHIND THE B757 ON TXWY M. IF ATC NEVER ISSUED THE AMBIGUOUS INSTRUCTION; IT ALL WOULD HAVE WORKED OUT. AT 100 KTS AFTER LNDG; IT IS NO TIME TO TALK TO ATC. THERE IS A LOT GOING ON IN THE COCKPIT DURING THE ROLLOUT. SUPPLEMENTAL INFO FROM ACN 458111: I CALLED THE TWR UPON LNDG/PARKING AND SPOKE WITH THE SUPVR. THE SUPVR STATED THE CTLR ISSUED YET ANOTHER INSTRUCTION TO MAKE A 'HARD R' TURN BEHIND COMPANY (TO TRY AND SALVAGE THE GAR). I EXPLAINED WE NEVER HEARD THAT XMISSION. IT WOULD BE BETTER AND SAFER TO LET PLT COMPLETE ROLLOUT AND NOT BE ISSUED TURNOFFS! HAD NO INSTRUCTION BEEN GIVEN; WE WOULD HAVE EXITED AT THE POINT CTLR WANTED. THE INSTRUCTIONS THE CTLR WAS ISSUING WOULD HAVE CAUSED RAPID AND UNSAFE CTL MOVEMENTS HAD WE COMPLIED AS THEY WERE ISSUED.