Low rumbling is an excellent candidate for active cancellation. But you won't be able to cancel the high-pitched metal rubbing past metal squeals, so it is probably not worth bothering about.
Basically active cancellation works well for long wavelengths and poorly for short wavelengths, where long and short are relative to the size of the area over which you wish to cancel the noise. Which is why cancellation with headphones is better, more frequencies have long wavelengths compared to the volume enclosed by the headphones -- and -- as someone else already pointed out, the high frequency crud can be blocked by the headphones.
You are more likely to succeed in buying the company operating the dumpster pickup and rescheduling their services than to block/cancel such noises.
Sorry.