If this were a bit more length and had some more specifics, I would love to show any non-technical manager this article. Having worked in both a start-up and a corporate software job, I saw the black and white with regards to technical debt.
The corporate job's code was never refactored, they just pile on more and more, monkey-wrench fixes when they need to and just wrestle code into their specs. Doing what should be really simple things takes forever, and onboarding is a nightmare. I can't stress the importance of refactoring enough, if you have clean organized code, new people can come in and make sense of it all and get to work.
As for management and the less technical, I like telling them that we could see performance improvements with refactoring (which is often true) so that they don't think it's completely useless on a product level. It takes a keen manager to notice that work pace slows when technical debt accrues.