Since dimension doesn't depend on magnitude. Hence, if a relation is dimensionally correct then it doesn't mean that it will also be mathematically or physically correct.
What will be the vice-versa?
Please answer these three questions.
Q1. If a relation is dimensionally incorrect, can it be mathematically correct?
Q2. If a relation is mathematically correct, can it be dimensionally incorrect?
Q3. If a relation is mathematically incorrect, can it be dimensionally correct?
https://youtu.be/AbB_j4uPNrM?t=65 <--- check out the video for reference, watch it till the 4th minute and listen to the last statement carefully.
Dimensional analysis is a heuristic you can use to check whether a relation is "obviously wrong". Checking that the dimensions are correct is like checking whether your answer is positive when you expect a positive answer. You can probably answer your own questions by replacing "is dimensionally correct" with "has the correct sign".
Q1: If a relation has the wrong sign, can it be mathematically correct?
Q2: (This is actually the same as Q1).
Q3: If a relation is mathematically incorrect, can it still have the same sign?