Will 220v 50 Hz BLDC Washing Machine work with 240v 60 Hz?
BLDC ? Normally when talking BLDC my thoughts go to Motors you are talking Brushless Direct Current [Brushless DC] motor. Which means that motor is controlled differently - Voltage is converted to DC and you either have a direct connection where voltage controls RPM or a VFD style motor controller that determines RPM. 

Now back to that BLDC motor - it would be using a Controller to operate that motor - and as such depending on what type  of controller and how its supply circuits are it could over drive the motor - burn up both motor and controller. 

In a washing machine the Motor is generally AC , but not always anymore..
Now on to the deal between 50Hz AC and 60Hz AC at 60 Hz your motor will run faster about 20% faster, you will use more power as well [see next paragraph for important information] - approximately 20% more.

You will also draw more current and might exceed the FLA [Full Load Amps] of the motor - what does that mean .. it means you will let the smoke out of the motor and the aroma will not be pleasant - nor the expense. They have yet to create any device to put the smoke back into a motor once it is blown and fried so you would need to buy a new motor. Now frying a motor if it goes up in flames while you went outside somewhere - perhaps your home burns with it.. is it worth saving a few pieces of silver IMO no.

Given that the unit you want is made in China I would imagine the FLA barely meets the requirements for the 50Hz threshold - so at 60Hz you would exceed the FLA. 

In short - Don't do this..

EDIT 12/13/2017
If you insist on doing this :
You can solve all the problems surges, brownouts and the voltage / frequency issue in another way.

Purchase a battery backup unit or Inverter of sufficient amperage to support operating your washer. 240VAC/60hz input 220VAC /50hz output.

Of course that might defeat your intent to save on costs..