Well, besides simply changing the names of the table and columns and the values inserted, you actually made two significant changes to my example. Using your names and values, the LIKE (not equals) still fails to produce any rows.
In case you liked those names and data values better than the ones in my example, try this version:
mysql> set @@sql_mode = 'STRICT_TRANS_TABLES,NO_ENGINE_SUBSTITUTION';
Query OK, 0 rows affected (0.00 sec)
mysql> select version(), @@sql_mode;
+-----------+--------------------------------------------+
| version() | @@sql_mode |
+-----------+--------------------------------------------+
| 5.1.73 | STRICT_TRANS_TABLES,NO_ENGINE_SUBSTITUTION |
+-----------+--------------------------------------------+
1 row in set (0.00 sec)
mysql> drop table if exists data;
Query OK, 0 rows affected, 1 warning (0.01 sec)
mysql> create table data ( stringvalue varchar(32)) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE=utf8_unicode_ci;
Query OK, 0 rows affected (0.01 sec)
mysql> insert into data set stringvalue='Thor\'s Hammer';
Query OK, 1 row affected (0.00 sec)
mysql> insert into data set stringvalue='Thor\\''s Hammer';
Query OK, 1 row affected (0.00 sec)
mysql> select * from data;
+----------------+
| stringvalue |
+----------------+
| Thor's Hammer |
| Thor\'s Hammer |
+----------------+
2 rows in set (0.00 sec)
mysql> select * from data WHERE stringValue like '%\\%' escape '\\';
Empty set (0.01 sec)
mysql> select * from data WHERE stringValue like '%\\\\%' escape '\\';
Empty set (0.00 sec)
You can keep adding more backslash escapes, but that doesn't help.