Venting A Low Pitched Roof

[DIMyself]

Long time reader, first time poster...

I have a very low pitched roof that butts up on two sides to well pitched sections. I have a rubber roof on the low pitched area now, and it's survived leak free so far. Problem was the previous roof leaked and had no ventillation. Obiouvsly then it'd drip whenever it warmed.
I can add vents to the soffet (will have to drill out some holes to get air into the roof cavity), but where the near-flat reaches the pitched, I can't seem to get enough of a cavity for air to flow to the main attic area.

Can vents be placed safely onto the "higher" part of the low pitched roof? Any venting would be seam taped down, and I assume it'd take a lot of weird water movement to get up and back down inside of a typical square vent?
Is this common or a complete no-no?

We do get all 4 seasons and while rare, 12"+ snow storms show up every 3 or 4 years.

Thank you all for your response!

[HayZee518]

for something with a low pitch, perhaps gable vents would be better. since you have a membrane roof already, I'd be hesitant to tear into it at the ridge line just for a vent.

[DIMyself]

Thanks for the reply.
Yeah, I'd hate to cut the membrane, but I can't think of many options. There's no space for any gable vents for the low sloped part. This roof used to be over a porch back in the day, so it's only as thick as the rafters.

I made a crude diagram here. Got my low sloped membrane roof. Meets on two sides well pitched parts of the roof. I put the hi and lo slope of the low pitched part on there.
I can vent the soffet on the bottom of our diagram, but I can't get air up and under the 'solid line' to meet up with the main attic where there are ridge vents. I thought about wedging myself inside the attic to drill holes, but that seems near impossible. Too tight.


meets pitched
____________
'hi end' | |
| |
| low sloped | meets pitched
'lo end' | |
-can vent soffet
on this edge

I fell like I'm boxed into a corner. Can vents be put on the 'higher' end of the low pitched part? I guess I've seen skylights for flat roofs and all, but never really seen vents on a low pitched house. I just fear it not sealing down perfectly or moisture getting in may make it worse. Plus being up near a steeper slope just doesn't sound great for melting snow. But am I right that it would take some extremely smart water to actually penetrate up and through a typical box vent, etc? I'd just have to worry about the process of sealing it down?

Thank you very much. I'll check back frequently in case my descriptions are confusing!

[DIMyself]

Sorry, hope this works!

..........meets pitched
..........____________
'hi end' ||||||||||||||
..........||||||||||||||
..........|||||||||||||| meets pitched
'lo end' ||||||||||||||

-can vent soffet
on bottom edge