Gutters in Longwood's HOA communities and shared buildings
Longwood has many named HOA communities, and in them the question is often not how to clean gutters but who decides.

Who owns the problem
In an HOA or a condo association, the recorded declaration says which parts of a building belong to the association and which to the owner. Gutters and downspouts may fall on either side, so reading that document comes before hiring anyone.
Communities in this area include Sabal Point, Alaqua Lakes, Sweetwater Oaks and The Springs. We have no information on what any of their documents say, so check yours or ask the management company.
Rules that can affect the work
An architectural review committee draws its power from the governing documents, and a denial should point to the rule it relies on. Sweetwater Oaks, for example, has an ARB Committee. Cleaning generally does not change appearance, but replacing or recoloring gutters might.
The Springs is gated, so a visit may need gate access arranged ahead of time. Tell the provider about it when you request the quote.
Drainage that is not yours or the city's
Not every drain belongs to the city. In communities where the roads and drainage are privately owned, the county may not be able to step in with public funds, so clogs are the community's to deal with.
Roof water that reaches a shared system should leave the building clean, which is one reason associations ask for downspout checks before storm season.
Clear it before the rain does the sorting
Request a free quote and an independent Longwood provider should follow up to confirm scope and price.