Let $X$ and $Y$ be independent random variable with respective moment generating function

$M\_x(t) = \frac{(8+e^t)^2}{81} $ and $M\_y(t) = \frac{(1+3e^t)^3}{64} , -\infty<t<\infty $

Then $ P(X+Y = 1) $equals

I know that using moment generating function we can find probability

$M\_x(t) = P(X=0)e^{t\*0} + P(X=1)e^{t\*1}.....P(X=n)e^{t\*n}$

Comparing this mgf we can get the particular probability.
But how do we do this question?