ewemli's answer is in the right direction but you should be combining FULLTEXT and soundex mapping, not replacing the fulltext, otherwise your LIKE queries are likely be very slow.
create table with_soundex (
id INT UNSIGNED AUTO_INCREMENT NOT NULL PRIMARY KEY,
original TEXT,
soundex TEXT,
FULLTEXT (soundex)
);
insert into with_soundex (original, soundex) values
('add some test cases', CONCAT_WS(' ', soundex('add'), soundex('some'), soundex('test'), soundex('cases'))),
('this is some text', CONCAT_WS(' ', soundex('this'), soundex('is'), soundex('some'), soundex('text'))),
('one more test case', CONCAT_WS(' ', soundex('one'), soundex('more'), soundex('test'), soundex('case'))),
('just filling the index', CONCAT_WS(' ', soundex('just'), soundex('filling'), soundex('the'), soundex('index'))),
('need one more example', CONCAT_WS(' ', soundex('need'), soundex('one'), soundex('more'), soundex('example'))),
('seems to need more', CONCAT_WS(' ', soundex('seems'), soundex('to'), soundex('need'), soundex('more')))
('some helpful cases to consider', CONCAT_WS(' ', soundex('some'), soundex('helpful'), soundex('cases'), soundex('to'), soundex('consider')))
select * from with_soundex where match(soundex) against (soundex('test'));
+----+---------------------+---------------------+
| id | original | soundex |
+----+---------------------+---------------------+
| 1 | add some test cases | A300 S500 T230 C000 |
| 2 | this is some text | T200 I200 S500 T230 |
| 3 | one more test case | O500 M600 T230 C000 |
+----+---------------------+---------------------+
select * from with_soundex where match(soundex) against (CONCAT_WS(' ', soundex('test'), soundex('some')));
+----+--------------------------------+---------------------------+
| id | original | soundex |
+----+--------------------------------+---------------------------+
| 1 | add some test cases | A300 S500 T230 C000 |
| 2 | this is some text | T200 I200 S500 T230 |
| 3 | one more test case | O500 M600 T230 C000 |
| 7 | some helpful cases to consider | S500 H414 C000 T000 C5236 |
+----+--------------------------------+---------------------------+
That gives pretty good results (within the limits of the soundex algo) while taking maximum advantage of an index (any query LIKE '%foo' has to scan every row in the table).
Note the importance of running soundex on each word, not on the entire phrase. You could also run your own version of soundex on each word rather than having SQL do it but in that case make sure you do it both when storing and retrieving in case there are differences between the algorithms (for instance, MySQL's algo doesn't limit itself to the standard 4 chars)