If you speak or write intelligibly, people can follow you. This adverb belongs with intelligible: it tells you how the talking or writing is done, not how clever the person is. You will see it more in careful English — classrooms, reports, instructions — than in chat. “Speak intelligibly” is close to “speak so people can understand you.” Clearly can also mean “in a bright way” or “obviously”; intelligibly stays with “so that it can be understood.”