6. (10 points) As shown in the figure, a rectangular block with dimensions $15 \mathrm{~cm}, 5 \mathrm{~cm}, 4 \mathrm{~cm}$ has a smaller rectangular block with dimensions $y \mathrm{~cm}, 5 \mathrm{~cm}, x \mathrm{~cm}$ (where $x, y$ are integers) cut out from it. The remaining volume is $120 \mathrm{~cm}^{3}$. What is $x+y=$ $\qquad$ .
【Analysis】The volume of the cut-off rectangular prism $=$ the volume of the larger rectangular prism - the volume of the remaining part. Based on this, we list the expression $15 \times 5 \times 4$ - 120 to find the volume of the cut-off rectangular prism. Then, given that $x, y$ are integers, we can solve the problem using the properties of integers.

【Solution】Solution: $15 \times 5 \times 4-120$
$$
\begin{array}{l}
=300-120 \\
=180\left(\mathrm{~cm}^{3}\right)
\end{array}
$$

Then $5 x y=180$, which means $x y=36$,
Since $x, y$ are integers, and $0<x<4,0<y<15$,
Therefore, $x$ is $3 \mathrm{~cm}, y$ is $12 \mathrm{~cm}, x+y=15 \mathrm{~cm}$.
The answer is: 15.