Cryptic crossword clue
Lunatic fringe—a cult moving away from the middle 11

The most common and most likely answer to this crossword clue is the 11 letter word CENTRIFUGAL

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Buddy explains!

The straight part
We know that "moving away from the middle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moving away from the middle = centrifugal.
The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does CENTRIFUGAL mean?

CENTRIFUGAL noun
  1. A rotating machine used to separate massecuite into sugar crystals and molasses.
CENTRIFUGAL adjective
  1. Tending, or causing, to recede from the center.
  2. Expanding first at the summit, and later at the base, as a flower cluster.
  3. Having the radicle turned toward the sides of the fruit, as some embryos.

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