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Kim Zolciak went nuts at LAX Monday night, claiming Delta was trying to separate her from her luggage -- but the trouble really started when she kinda bombed on 'Dancing with the Stars."

Kim was irate ... it appears she checked in for her flight at the last minute and the ticket agent said it was too late to check luggage.

Kim, who's on "Dancing with the Stars," protested, saying she has a lot of expensive stuff that could get lost. One of her people also went ballistic ... apparently he didn't get a boarding pass.

She went on Twitter to express her displeasure.

Kim's people tell us the mix-up was all over boarding passes ... that Delta couldn't find them for her daughter and hairstylist on the 10:10 PM flight. She says they all got re-booked on the 11:45 PM flight, but then her daughter got bumped to the wait list. Kim's rant was effective -- everyone eventually ended up getting on the 11:45 PM.

Apparently the folks at Delta didn't see the 'DWTS' premiere. If they had, they might have expected her to have a short fuse.