GNU Make implicit rules

I wish to build both debug and release builds of my programs with
a makefile (simplified version below).
I have a problem when using implicit rule though in that I wish to
have separate CFLAGS for both my debug and release builds.
How should I specify implicit rule correctly so that my CFLAGS_DBG
gets picked up when building the debug target?
Any help with this appreciated.

CC = g++
CFLAGS = -O3 -I/usr/include/SDL -I/usr/X11R6/include
CFLAGS_DBG = -O0 -g -I/usr/include/SDL -I/usr/X11R6/include
LDFLAGS = -L/usr/X11R6/lib -lSDL -ldl -lm -lX11

OBJECT = main.o dialog.o cfgparser.o sprite.o ai.o actor.o

release: $(OBJECT)
$(CC) -o release.bin $(LDFLAGS) $(OBJECT)

debug: $(OBJECT)
$(CC) -o debug.bin $(LDFLAGS) $(OBJECT)

..cpp.o:
$(CC) -c $(CFLAGS) $<

all: release

.

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