6. The numbers $a, \beta$ satisfy the following equations: $\alpha^{3}-3 \alpha^{2}+5 \alpha=1$, $\beta^{3}-3 \beta^{2}+5 \beta=5$. Then, the value of $\alpha+\beta$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 5
6. B.
$$
\text { Let } \begin{aligned}
f(x) & =(x-1)^{3}+2(x-1) \\
& =x^{3}-3 x^{2}+5 x-3,
\end{aligned}
$$

Now $g(y)=y^{3}+2 y$.
For $\alpha$, we have $g(\alpha-1)=f(a)=\alpha^{3}-3 \alpha^{2}+5 \alpha-3$
$$
\begin{aligned}
& =1-3=-2, \\
g(\beta-1) & =f(\beta)=\beta^{3}-3 \beta^{2}+5 \beta-3=5-3=2 .
\end{aligned}
$$

Since $g(y)$ is a monotonic odd function, we know $\alpha-1=-(\beta-1) \Rightarrow \alpha+\beta$ $=2$.