The following is a video of a “super flush,” a toilet that is strong enough to flush anything with ease. While you won’t be flushing this many carrots down your toilet anytime soon, this will sure be enough of a flush for what you need.
The most powerful toilet commercially available is the American Standard Champion toilet series. They designed a completely new way to flush so that you would never need a plunger again. They say that using objects like these aren’t realistically what you’d be flushing, but if they used what actually goes down the toilet to show off the product it would be a little too gross.