For the next person who goes through this, in our relatively small database, the request is:
SELECT * FROM table_name WHERE field LIKE 'some-field-search-value'; ... Result row Returns 1 row in set (0.00 sec)
Compared with:
SELECT * FROM table_name WHERE field LIKE BINARY 'some-field-search-value'; ... Result row Returns 1 row in set (0.32 sec)
In short, at least for our database (MySQL 5.5 / InnoDB) there is a very significant performance difference between the two searches.
Obviously, this is a mistake in MySQL 5.5: http://bugs.mysql.com/bug.php?id=63563 and in my testing on the same database in MySQL 5.1, the LIKE BINARY query still uses the index (while in 5.5, it performs a full table scan.)
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