When you get your values from your $_POST insert them in with a mysql insert multiple values like this:

insert into myTable 
    (someColumn, someOtherColumn) 
values 
    (someValue1, someOtherValue1), 
    (someValue2, someOtherValue2), 
    (someValue3, someOtherValue3)

Edit: If you want the in one row use something like PHP implode():

$qry="insert into mytable (someColumn) values (".implode(',',$myArray).")

Not that you want to make sure that the $myArray variable is clean of anything that could SQJ Injection attack you database. A prepared statement would be a suggestion.

Django models come with JSONField() which you could use to serialize the list of integer values and later deserialize it into a list.

Another appproach is: if you have limited number of options, you could also try creating separate column for each option in your database instead of saving them in single field separated by comma.

E.g

interest_executive: Boolean
interest_manager: Boolean
interest_service_advisor: Boolean

Finally, another approach is to create a separate table and have foreign key relationship between user_id and interest_name_id but this would be overkill if you have limited number of interests.