Maintenance & Pruning
It looks to me that the old plant matter with the yellow line on it is old dead stem. It needs to be removed. The one with the green line appears to be a live viable stem to the right of the root, and dead to the left. It needs to be trimmed off at the yellow arrow. If the root is viable, leave it.
This guy (the Monster Monstera) is really ripe for a good trim. Between May 1 - May 15, remove all stems with leaves. The areas with the yellow circles around them are where you want to trim them.
You can see that the stems sprouted from an old leaf junction. You want to cut above or beyond that. Leave at least 1 or two old leave junctions attached to the stems you leave in the dirt. This is where new growth will start. The red arrows indicate the general area where you want to remove.
Get a 6" pot and plant all the stems you remove in it. Make sure you have at least 1 old leaf junction (preferably 2) both above and below the dirt on each stem. Below the dirt this is where the new roots,start, above the dirt, new shoots. On both ends you only need about 1" of stem left beyond each leaf node. Trim them back to get rid of unwieldy dead stem material.
This guy is doing fine. Give him a shower, remove any dead plant matter from the soil, and top dress a tiny bit. Get a 5' or 6' plant stake and just shove it right down the center of the pot. Get some plant tie tape and start tying the stems to it to encourage them to grow up and not out. Lead any air roots (indicated by yellow arrow) back to the soil. That will help the leaves beyond it on the stem get larger. Fertilize him with the Miracle Grow Garden Feeder