Leaving a job without a 2 week notice because the other company needs me to start ASAP.

Hello!

So I usually don't do this, I always give a minimum of 2 weeks notice and at times 3 weeks, mainly because when I was a manager that is what I liked and expected. I recently got a job offer from a company where the position is a lot better (going from customer service to a project related role) and a much better pay. The issue is the company needs me to start ASAP, I am trying to figure out how to let my company know that I won't be there next week onwards without ruining that relationship because the managers there were truly amazing.

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