Suppose the graph of $f(x)=x^4 + ax^3 + bx^2 + cd + d$, where $a$, $b$, $c$, $d$ are all real constants, passes through three points $A \big(2,\frac{1}{2}\big)$, $B \big(3, \frac{1}{3}\big)$, and $C \big(4, \frac{1}{4}\big)$. Find the value of $f(1) + f(5)$.