Dual Flush Toilet Clogged?

I have a dual toilet. How can the toilet be fixed from flushing solids down the liquids drain?

I have already noticed the problem is that the solids are clogged, but the entire toilet still flushes and bowl stops when full of water. The tank won't stop filling with water, so I turned off the water to the toilet currently, to stop wasting water.

By Fronz D. from Toronto, ON