If $f(x)=x^{2}+bx+c$ where $b,c$ are integers and it is given that $f(x)$ perfectly divides $x^{4}+6x^{2}+25$ and $3x^{4}+4x^{2}+28x+5$, what is the value of $f(1)?$

Note-This question is taken from SOF-IMO

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