How to upgrade Mysql 5.5 to 5.6 without data loss on aws-ec2?
You don't need to dump and import the databases, a copy of the folder /var/lib/mysql should be ok for backup.
I suggest you upgrade to MySQL 5.7 as its the currently supported release and has better performance,
here are the steps, I implemented it many times with no issues
1. # service mysql stop


backup your databases before the upgrade
$ cp /var/lib/mysql /var/lib/mysql.original

Download the MySQL 5.7 RPM
$ wget http://repo.mysql.com/mysql57-community-release-el7.rpm -P /tmp/

Remove the MySQL-Community RPM that contains MySQL 5.5
$ yum remove mysql-community-release

Install the MySQL 5.7 RPM
$ rpm -ivh /tmp/mysql57-community-release-el7.rpm

Update the MySQL Repository to 5.7
$ yum update mysql

Let MySQL know that it received an upgrade
service mysql start
mysql_upgrade