No vent for drain waste line.

I have some issues with draining around my new home. I've noticed again there isn't a vent for the main line and instead air admittance valves on the kitchen sink and the washer drain. None in the bathroom I don't beilve. All the drains are slow and the washer was draining and the kitchen sink was gurgling untill I heard a huge bang and the washer blew the pipe right out and drained all over.. so I geuss my question is what can I do to try and help with this issue and what would a rough estimate be to add a main vent off the stack in a house with a basement 2 floors and an attic?(4 floors) Is this worth it to add in? What are some other issues that may cause this if any? Thanks in advance! Sorry if I come off Abit of a newb.. I kinda am.. [emoji18]

your kitchen sink has no vent it is plumbed using a double wye instead of a cross



the washing machine pipe was installed with out using cleaner, they used only glue
the joint came apart,

I am thinking that you have a slow/clogged drain line.

Flushed the toilet this morning and the sink was gurgling loud and all the water all over my basement through the disconnected washer.. called the plumber who found roots and roots and more roots in my main to the street lol.. got that taken care of but the sink still gurgles when it's flushed any thoughts?

If it is just that sink, and it only gurgles when you drain that sink, then yes, that jacked up vent is the problem, and you need to get it fixed like frodo showed with his Van Gogh.

If it gurgles when something else drains, than you still have some clogging issues going on.

Correction all day everything was going away fine and all the sudden the washer drain starts overflowing and I stopped the washer. Everything up stairs drains FINE not slow or anything. But all comes out of the washer drain.. now again I had a plumber out Saturday and he "claims" he cleaned the main out to the street and it did work all last night and all day today? Why would it all the sudden stop flowing again!?! Could a pipe under ground have collapsed due to them being snaked? What are some possibilities?!? This is really getting old. I can't keep going to the gas station to use the facilities lol.. thanks in advance!

a drain line that is full of grease and junk. when you insert a sewer machine it pokes threw the grease then when you pull it back the grease
will fill the hole in again

this is what you need to do. Have a company video your drain line, the video will show where and what the problem is.
you have a blockage, plane and simple,