You can convert these numbers to ordinary numbers with:
SUBSTRING_INDEX(column, '.', 1) + IF(LOCATE(column, '.'), SUBSTRING_INDEX(column, '.', -1)/6, 0)
You can then use this expression in SUM()
to add all the column in the table, or you can use it with +
to add different columns to each other. E.g.
SELECT SUM(SUBSTRING_INDEX(column, '.', 1) + IF(LOCATE(column, '.'), SUBSTRING_INDEX(column, '.', -1)/6, 0)) AS total
FROM yourTable
If you also need to convert the sum back to your base 6 fraction representation, you can use:
CONCAT(FLOOR(total), '.', ROUND(MOD(total, 1) * 6)
So a full query might look like:
SELECT CONCAT(FLOOR(total), '.', ROUND(MOD(total, 1) * 6) AS total
FROM (SELECT SUM(SUBSTRING_INDEX(column, '.', 1) +
IF(LOCATE(column, '.'), SUBSTRING_INDEX(column, '.', -1)/6, 0)) AS total
FROM yourTable) as subquery