To solve the equation, let's simplify it step by step:

1. Start by simplifying the expressions inside the square roots:
căn(x-1) - Let's call this expression A.

2. Rewrite the equation using the simplified expressions:
căn(x+3-4A) + căn(x+8-6A) = 1

3. Combine the square roots with the same expression inside:
căn(x+3-4A) + căn(x+8-6A) = 1

4. To eliminate the square roots, square both sides of the equation:
(căn(x+3-4A) + căn(x+8-6A))^2 = 1^2
(x+3-4A) + 2căn(x+3-4A)căn(x+8-6A) + (x+8-6A) = 1

5. Simplify the equation:
2x + 11 - 10A + 2căn(x+3-4A)căn(x+8-6A) = 1

6. Rearrange the equation:
2x - 10A + 2căn(x+3-4A)căn(x+8-6A) = -10

7. Move all the terms to one side of the equation:
2x - 10A + 2căn(x+3-4A)căn(x+8-6A) + 10 = 0

This is the simplified form of the equation. It cannot be solved further without additional information or specific values for x and A.