Slop Sink Backing Not Always Draining

[manor]

I have a slop sink in my basement and the washer also drains into the sink. Now running some water it drains fine, the problem comes when doing laundry. Sometimes its fine and there are no problems. Other times the first time the washer drains in a cycle it drains out of the sink but on the second rinse it backs up. The slop sink drains into a cast iron pipe which goes to a drywell outside. The trap to the sink is clear. When the sink doesnt drain i can repeatly plunge it and it will go down. Any ideas?
Also:
1: There is no vent tied into it.
2. When I plunge it some air bubbles come out of the drain
3. If the drywell was full how would I be able to get it to go down by plunging?

[Plbgbear]

It's been in my experience that dry wells are usually meant for small sinks and condensate drains. The amount of discharge they receive from the above mentioned are not producing a large amount of waste, therefore not filling the drywell up fast enough. In other words, the drywell has enough time to absorb the waste and not fill to the top. A washing machine will discharge alot of water at one time possibly causing the drywell to fill up and not leave any room for more waste. Have you taken a look to see if the drywell overflows when the sink backs up. Also, how big is your drywell. Maybe it's not meant to receive that much discharge.