MySQL/Amazon RDS error: "you do not have SUPER privileges..."

I'm attempting to copy my mysql database from an Amazon EC2 to an RDS:

I successfully did a mysqldump of my database into my root folder using this:

root@ip-xx-xx-xx-xx:~# mysqldump my_database -u my_username -p > my_database.sql

Then I tried to transfer this .sql file to my new RDS database:

root@ip-xx-xx-xx-xx:~# mysql my_database -u my_username -p -h  my_new_database.xxxxxxxxx.us-east-1.rds.amazonaws.com < my_database.sql

Unfortunately, I get following error message:

You do not have the SUPER privilege and binary logging is enabled (you *might* want to use  the less safe log_bin_trust_function_creators variable)

I tried to GRANT SUPER.. in a variety of ways but I'm getting errors when I try to do that too. Typing mysql > FLUSH privileges; doesn't work either.

I'm a mysql beginner so sorry for such an easy question. Thoughts?