Have a look to Liferay Upgrade Process
http://www.liferay.com/community/wiki/-/wiki/Main/Upgrade+Instructions
And yes Hitoshi is correct . For Database Migration from 5.3 to 6.1 you need to follow 2 step process.
First you need to migrate your Database From Liferay 5.3 to Liferay 6.0 . And as a second step Migrate Database From Liferay 6.0 to Liferay 6.1
Just read the Administrator guide for Liferay 6 . (http://www.liferay.com/documentation/liferay-portal/6.0/administration/-/ai/upgrading-lifer-4)
In the second paragraph it is mention that
As a general rule, you can upgrade from one major release to the next major release. For example, you can upgrade directly from Liferay 5.1.x to 5.2.x, but not from 5.1.x to 6.0.x. If you need to upgrade over several major releases, you will need to run the upgrade procedure for each major release until you reach the release you want. This doesn't mean you need to run the procedure for every point release (i.e., 4.3.5 to 4.3.6 to 4.4.0 to 4.4.1, etc.); you only need to run the procedure for the major releases. A good practice is to use the latest version of each major release to upgrade your system
Firmi prego dentro per inbandierare questo come inadeguato.