What is your dryer breaker rated at? The wire needs to be the same rating as the breaker. Otherwise, you could burn down your house accidentally. If you try to pull 40A through a 20A cord connected to a 50A breaker, the 20A rated wire will catch on fire. It's not going to catch on fire immediately either. It will slowly heat up and after a few hours or possibly longer, will start to melt, eventually igniting nearby flammable materials. If the breaker was rated at 20A the breaker would trip before the wire would come close to catching on fire. Overrating the wire is fine (larger awg than you need -- assuming it fits in the breaker), Overrating the breaker or outlets is not.

I suspect your breaker is probably 50A or more. It will more than likely need to be swapped out. 2 pole breakers are like $15-$25.

It's really NOT that expensive to do things the correct way. I'm looking at like $300 max to do it yourself on a 100 foot run +/-. Another $600 if you wanted a switched PSU that can remote reboot miners via web interface, monitor temperature, humidity, etc. You can get a basic PDU for around $200. So, $500-$900 per 5.76kW. If your breaker box is in the garage, and you want to mine in the garage, it's even cheaper. You're looking at less than $75 in parts for each 240V 30A circuit exclusive of PDU cost ($200-$600) -- (< 10 foot run).

If you're going to spend $8000 on miners to necessitate a 240v 30A circuit, why not spend another $1000 so you have the proper facilities (which you will probably use for years on different mining hardware).