Quitting a job before the "two months"

Hi there,
I`m currently working in an IT company in Prague and I`ve been offered a position abroad.
The problem is this two month-notice, which are not 60 days, as it is EXCLUDED the current month, you know, the Czech Labor code.
It means that I would need to start this new job in June and the company not based in Czech Rep doesn`t want to.
So my fear is that my current management won`t accept me leaving before these terms..

My question is, what if a written agreement is not reached and somebody quit before anyway? Are there in it any legal implication in Czech Republic? Note that there is nothing about an early leave in my contract, just that the contract is based on the current legislation.

Of course the risk to not be re-employment in the same company is already taken into account.

So has anybody had any experience about it?

Thank you.

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