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Dickson, on loan from Southampton, was sent off during the second half of the 3-1 defeat at Bramall Lane for a reckless challenge on United's opening goalscorer Lee Williamson.
It was the left-back's second dismissal during his time with Orient and he has been hit with a four-match suspension.
Russell Slade's side have three League One matches remaining this campaign, meaning Dickson will also have to miss a game next season.
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