i haven’t heard of such formula ,but anyway if both of your pipe slopes are above minimum to get self-cleansing you shouldn't worry about debris.
i'v done design and construction for several sewer projects ,we've never changed a slope without a manhole ,but i can't see why not, as long as both of the lines are at a grade steep enough to achieve self-cleansing velocities at the designed proportional depth, which is based on your very near expected flow.
self-cleansing velocities is very important ,but practically you can't always get it ,specially at the very upstream part of a system ,if you insist on flushing upstream you will end up with a massive excavation work downstream.