Find the shortest unique sublist
Husk, 12 14 15 bytes
+3 bytes for case [[1,1]]
Ṡḟȯ¬€Ṡ-uÖLṁȯtuQ

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Explaination
          ṁ      -- map and concatenate
           ȯt    --   all but the first
             u   --   unique elements of
              Q  --   contiguous sublist
        ÖL       -- sort by length
Ṡḟ               -- find the first element satisfying this predicate
  ȯ¬€            --   not an element of
     Ṡ-          --   the list of sublists minus
       u         --   its unique elements

Note: Ṡ f g x = f (g x) x and this is hard to explain using the method above.